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PGP PUBLIC KEY BLOCK: [david2@localhost ~]$ gpg2 –export –armor “David Bernier (doubledeckerpot7) “

—–BEGIN PGP PUBLIC KEY BLOCK—–
Version: GnuPG v2

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cuxZSn8KQn84iAtLDK2fxD9iX7USkQvTy32TLcoQUOhapY5VUR0RpORcTYzKjnT2
vN5bGLTEgXUrnf5cE7fnueX8VpeVjx1IiAhAOJrMSvXWto57XFoFxStMeKpbZd5G
bHXGOT60OERhdmlkIEJlcm5pZXIgKGRvdWJsZWRlY2tlcnBvdDcpIDxkYXZpZDI1
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hJojtILupblVD98WS9rYnvSzEPRrl2rlfknzfBrtT2irx68HEvedAf9hVWQyD4Bn
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xQ7yYJgONEhSDweIXCfgXyR8baP7ZnkiyuorsMjXZ3Ztkq70U/+dXqWVk5bBfzZB
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EQH/e3D0ZfIsebYlQac5CPfzOZ8SjgHTc9rUqX0+hE3C9TBKVSsjP8eFkzGrYZLi
6fXRbx0d7i0upBx6s/ZABhHWtAH/UD+z2LgUi3NvMqlzE4ajhvyqlYCWqrxulveU
PiN+JUnzXdScCrbt7odpNZpYyitXTO7i3SDsWtmID9rfzjTXTw==
=pvTe
—–END PGP PUBLIC KEY BLOCK—–

Written by meditationatae

March 2, 2015 at 2:09 am

Posted in History

Formatted output of pi computation to about 9300 decimals in JS/Linux virtual Linux Box (Fabrice Bellard)

0003
14159265358979323846264338327950288419716939937510 50 decimals
58209749445923078164062862089986280348253421170679 100 decimals
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989 1000 decimals

38095257201065485863278865936153381827968230301952
03530185296899577362259941389124972177528347913151
55748572424541506959508295331168617278558890750983
81754637464939319255060400927701671139009848824012
85836160356370766010471018194295559619894676783744
94482553797747268471040475346462080466842590694912
93313677028989152104752162056966024058038150193511
25338243003558764024749647326391419927260426992279
67823547816360093417216412199245863150302861829745
55706749838505494588586926995690927210797509302955
32116534498720275596023648066549911988183479775356
63698074265425278625518184175746728909777727938000
81647060016145249192173217214772350141441973568548
16136115735255213347574184946843852332390739414333
45477624168625189835694855620992192221842725502542
56887671790494601653466804988627232791786085784383
82796797668145410095388378636095068006422512520511
73929848960841284886269456042419652850222106611863
06744278622039194945047123713786960956364371917287
46776465757396241389086583264599581339047802759009 2000 decimals

94657640789512694683983525957098258226205224894077
26719478268482601476990902640136394437455305068203
49625245174939965143142980919065925093722169646151
57098583874105978859597729754989301617539284681382
68683868942774155991855925245953959431049972524680
84598727364469584865383673622262609912460805124388
43904512441365497627807977156914359977001296160894
41694868555848406353422072225828488648158456028506
01684273945226746767889525213852254995466672782398
64565961163548862305774564980355936345681743241125
15076069479451096596094025228879710893145669136867
22874894056010150330861792868092087476091782493858
90097149096759852613655497818931297848216829989487
22658804857564014270477555132379641451523746234364
54285844479526586782105114135473573952311342716610
21359695362314429524849371871101457654035902799344
03742007310578539062198387447808478489683321445713
86875194350643021845319104848100537061468067491927
81911979399520614196634287544406437451237181921799
98391015919561814675142691239748940907186494231961 3000 decimals

56794520809514655022523160388193014209376213785595
66389377870830390697920773467221825625996615014215
03068038447734549202605414665925201497442850732518
66600213243408819071048633173464965145390579626856
10055081066587969981635747363840525714591028970641
40110971206280439039759515677157700420337869936007
23055876317635942187312514712053292819182618612586
73215791984148488291644706095752706957220917567116
72291098169091528017350671274858322287183520935396
57251210835791513698820914442100675103346711031412
67111369908658516398315019701651511685171437657618
35155650884909989859982387345528331635507647918535
89322618548963213293308985706420467525907091548141
65498594616371802709819943099244889575712828905923
23326097299712084433573265489382391193259746366730
58360414281388303203824903758985243744170291327656
18093773444030707469211201913020330380197621101100
44929321516084244485963766983895228684783123552658
21314495768572624334418930396864262434107732269780
28073189154411010446823252716201052652272111660396 4000 decimals

66557309254711055785376346682065310989652691862056
47693125705863566201855810072936065987648611791045
33488503461136576867532494416680396265797877185560
84552965412665408530614344431858676975145661406800
70023787765913440171274947042056223053899456131407
11270004078547332699390814546646458807972708266830
63432858785698305235808933065757406795457163775254
20211495576158140025012622859413021647155097925923
09907965473761255176567513575178296664547791745011
29961489030463994713296210734043751895735961458901
93897131117904297828564750320319869151402870808599
04801094121472213179476477726224142548545403321571
85306142288137585043063321751829798662237172159160
77166925474873898665494945011465406284336639379003
97692656721463853067360965712091807638327166416274
88880078692560290228472104031721186082041900042296
61711963779213375751149595015660496318629472654736
42523081770367515906735023507283540567040386743513
62222477158915049530984448933309634087807693259939
78054193414473774418426312986080998886874132604721 5000 decimals

56951623965864573021631598193195167353812974167729
47867242292465436680098067692823828068996400482435
40370141631496589794092432378969070697794223625082
21688957383798623001593776471651228935786015881617
55782973523344604281512627203734314653197777416031
99066554187639792933441952154134189948544473456738
31624993419131814809277771038638773431772075456545
32207770921201905166096280490926360197598828161332
31666365286193266863360627356763035447762803504507
77235547105859548702790814356240145171806246436267
94561275318134078330336254232783944975382437205835
31147711992606381334677687969597030983391307710987
04085913374641442822772634659470474587847787201927
71528073176790770715721344473060570073349243693113
83504931631284042512192565179806941135280131470130
47816437885185290928545201165839341965621349143415
95625865865570552690496520985803385072242648293972
85847831630577775606888764462482468579260395352773
48030480290058760758251047470916439613626760449256
27420420832085661190625454337213153595845068772460 6000 decimals

29016187667952406163425225771954291629919306455377
99140373404328752628889639958794757291746426357455
25407909145135711136941091193932519107602082520261
87985318877058429725916778131496990090192116971737
27847684726860849003377024242916513005005168323364
35038951702989392233451722013812806965011784408745
19601212285993716231301711444846409038906449544400
61986907548516026327505298349187407866808818338510
22833450850486082503930213321971551843063545500766
82829493041377655279397517546139539846833936383047
46119966538581538420568533862186725233402830871123
28278921250771262946322956398989893582116745627010
21835646220134967151881909730381198004973407239610
36854066431939509790190699639552453005450580685501
95673022921913933918568034490398205955100226353536
19204199474553859381023439554495977837790237421617
27111723643435439478221818528624085140066604433258
88569867054315470696574745855033232334210730154594
05165537906866273337995851156257843229882737231989
87571415957811196358330059408730681216028764962867 7000 decimals

44604774649159950549737425626901049037781986835938
14657412680492564879855614537234786733039046883834
36346553794986419270563872931748723320837601123029
91136793862708943879936201629515413371424892830722
01269014754668476535761647737946752004907571555278
19653621323926406160136358155907422020203187277605
27721900556148425551879253034351398442532234157623
36106425063904975008656271095359194658975141310348
22769306247435363256916078154781811528436679570611
08615331504452127473924544945423682886061340841486
37767009612071512491404302725386076482363414334623
51897576645216413767969031495019108575984423919862
91642193994907236234646844117394032659184044378051
33389452574239950829659122850855582157250310712570
12668302402929525220118726767562204154205161841634
84756516999811614101002996078386909291603028840026
91041407928862150784245167090870006992821206604183
71806535567252532567532861291042487761825829765157
95984703562226293486003415872298053498965022629174
87882027342092222453398562647669149055628425039127 8000 decimals

57710284027998066365825488926488025456610172967026
64076559042909945681506526530537182941270336931378
51786090407086671149655834343476933857817113864558
73678123014587687126603489139095620099393610310291
61615288138437909904231747336394804575931493140529
76347574811935670911013775172100803155902485309066
92037671922033229094334676851422144773793937517034
43661991040337511173547191855046449026365512816228
82446257591633303910722538374218214088350865739177
15096828874782656995995744906617583441375223970968
34080053559849175417381883999446974867626551658276
58483588453142775687900290951702835297163445621296
40435231176006651012412006597558512761785838292041
97484423608007193045761893234922927965019875187212
72675079812554709589045563579212210333466974992356
30254947802490114195212382815309114079073860251522
74299581807247162591668545133312394804947079119153
26734302824418604142636395480004480026704962482017
92896476697583183271314251702969234889627668440323
26092752496035799646925650493681836090032380929345 9000 decimals

95889706953653494060340216654437558900456328822505
45255640564482465151875471196218443965825337543885 9100 decimals
69094113031509526179378002974120766514793942590298
96959469955657612186561967337862362561252163208628 9200 decimals
69222103274889218654364802296780705765615144632046
92790682120738837781423356282360896320806822246801 9300 decimals
2248
“The Joy of Pi” online gives the block of 10 digits from number 9291 to 9300
as follows:

6822246801

On the Web:

http://www.joyofpi.com/pi.html

—————————–

Written by meditationatae

February 26, 2015 at 5:50 am

Posted in History

Raw output of pi computation to about 9300 decimals in JS/Linux virtual Linux Box ( Fabrice Bellard)

00031415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983052358089330657574067954571637752542021149557615814002501262285941302164715509792592309907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111790429782856475032031986915140287080859904801094121472213179476477726224142548545403321571853061422881375850430633217518297986622371721591607716692547487389866549494501146540628433663937900397692656721463853067360965712091807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862947265473642523081770367515906735023507283540567040386743513622224771589150495309844489333096340878076932599397805419341447377441842631298608099888687413260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Written by meditationatae

February 26, 2015 at 5:15 am

Posted in History

Colossally abundant number with prime factors 2 to 999,781,070,909

The program superabun3842a.out finished around January 6th. It searched for highly abundant numbers. The output was re-directed to a file. Afterwards, I wanted to check independently the values of log(N) and sigma(N)/N found by the program. Each N is given in shortened prime factorization form. In this form, adequate with non-increasing exponents for the primes, only the starting index and/or ending index for some exponent are given.

For example,

1 44
2 27
3 18
4 15
5 12
6 11
7 10
9  9
10 8
13 7
20 6
33 5
69 4
222 3
1673 2
106913 1

37599987402 0

is the number N where 2 has exponent 44, 3 has exponent 27, 5 has exponent 18, 7 has exponent 15, 11 has exponent 12, 13 has exponent 11, 17 and 19 have exponent 10. The number 19 is the 8th prime, and its exponent in the factorization of N is 10, the same as for the 7th prime 17. So we skip 8, and at the 9th prime, 23, the exponent is 9. For the 10th prime, the exponent is 8. The 11th and 12th primes also have exponent 8 in N. The 13th through the 19th primes have exponent 7 in N. The 20th through the 32nd primes have exponent 6 in N. The 33rd through the 68th primes have exponent 5 in N. The 69th through the 221st primes have exponent 4 in N. The 222nd through the 1672nd prime have exponent 3 in N. The 1673rd through the 106912nd primes have exponent 2 in N. The 106913rd through the 37599987401st primes have exponent 1 in N. The primes starting at the 37599987402 do not divide N. According to my calculations, the 37599987401st prime is 999,781,070,909 or just under 10^12 .  It took 40 hours independently to sum the logarithms of the primes from

2 to 10^12:

[david2@localhost eratosthenes7]$ time ./eratosthsiv3630a.out

size of int is: 4
size of long is: 8
size of char is: 1

pi(1000000000000) = 37607912018

sum_logs_primes = 999999030333.09622463699607903975308725646673
real 2365m37.094s
user 2364m50.247s
sys 0m2.488s

[david2@localhost eratosthenes7]$

The following command in the PARI/gp calculator,

? count = 37599987401; forprime(q=999781070910 , 1000000000000, count=count+1); count

%196 = 37607912018

implies that if pi(10^12) = 37607912018 then pi(999781070910) = 37599987401. Since 999781070909 is the last prime below 999781070910, 999781070909 is the 37599987401st prime.

Below, the PARI/gp command to sum the logs of primes from 999781070910 to 10^12:

? sumlogprimes=0; forprime(q=999781070910 , 1000000000000, sumlogprimes=sumlogprimes+log(q)); sumlogprimes
%199 = 218964392.249194594870107709322349966327713173580

Then, after Tchebychev,

? thetaCheb = 999999030333.09622463699607903975308725646673-sumlogprimes
%201 = 999780065940.847030042125971330430737290139016826

That is the sum of the logs of primes from 2 to 999781070909 inclusive, calculated in PARI/gp.

Then we calculate the critical exponent (CA numbers) for 999781070909: the largest epsilon for which 999781070909 has exponent 1 in C.A. numbers.

? p=999781070909
%204 = 999781070909
? epsilon
%205 = 8.6159474458768635875553049472001443044 E-15
? epsilon=log(1+1/p)/log(p)
%206 = 3.61994187188332908418733101506308857973891597465 E-14  <=== critical exponent where

999781070909 first attains exponent 1.

g =
(Y)->floor(log((exp((1+epsilon)*log(Y))-1)/(exp(epsilon*log(Y))-1))/log(Y))-1

as a PARI/gp function implements the Erdos-Alaoglu, or Erdos-Alaoglu-Ramanujan formula for the exponent of the prime Y for exponent or critical exponent epsilon.

? g(2)
%207 = 44
? g(17)
%208 = 10
? g(19)
%209 = 10

Next, we calculate contribution to log(N) of exponents larger than 1,

for primes with index 1 [that is , the prime two] to index 106912 inclusive:

? sum4=0; for(X=1,106912, sum4 = sum4+(g(prime(X))-1)*log(prime(X)))
? sum4
%215 = 1412045.01159541398434404224867771016684988078484

? prime(106912)
%212 = 1397233
? g(1397233)
%213 = 2    OK

? prime(106913)
%210 = 1397251
? g(1397251)
%211 = 1  Ok.

Then we need to add thetaCheb and sum4  to get log(N):

? thetaCheb+sum4
%217 = 999781477985.858625456110315372679415000305866707

The abundant numbers program is very long, and was developped in stages. It prints values of log(log(N)) for highly abundant N.

? log(thetaCheb+sum4)
%218 = 27.6308025700349926529916290589321648678391771498

The above is log(log(N)) for the colossally abundant N with critical exponent:

? epsilon=log(1+1/p)/log(p)
%206 = 3.61994187188332908418733101506308857973891597465 E-14

where

p=999781070909 , according to the check-program (short, simple).

The value of log(log(N)) computed by superabun3842a.out is marked by (*****) :

current step number = 17
quotient de Robin: 0.999999972115680424387739328044
loglog n = 27.630802570034992652991629058932                        (*****)
sigma(n’)/n’ = 49.212458972166029828348808887298
record step is at: 37599987401
log(log(n’)) = 27.630802570034992652991629058932                    (*****)
PARI/GP
?
log(thetaCheb+sum4)
%218 = 27.6308025700349926529916290589321648678391771498

log(log(n’)) = 27.630802570034992652991629058932 30 digits OK .

Robin upper bound = 49.212460344422001174357312333199
sigma(n’)/n’ = 49.212458972166029828348808887298

I still  would like to verify independently sigma(N)/N.

=============================================

==============================================

=================================
step at 1
step at 2
step at 3
step at 4
step at 5
step at 6
step at 7
step at 9
step at 10
step at 13
step at 20
step at 33
step at 69
step at 222
step at 1673
step at 106913
step at 37599987401

? for(X=1,1, print(X,” “, g(prime(X))));for(X=2,1000000, if(g(prime(X))<g(prime(X-1)),print(X,” “,g(prime(X)))))

1 44
2 27
3 18
4 15
5 12
6 11
7 10
9 9
10 8
13 7
20 6
33 5
69 4
222 3
1673 2
106913 1

time = 4min, 41,736 ms.
—————————————

? p2=999781070909
%194 = 999781070909

? factor(999781070909)
%195 =
[999781070909 1]
? count = 37599987401; forprime(q=999781070910 , 1000000000000, count=count+1); count
time = 2,294 ms.
%196 = 37607912018

? 37607912018
%197 = 37607912018

? p2
%198 = 999781070909
? factor(999781070909)
%195 =
[999781070909 1]

? count = 37599987401; forprime(q=999781070910 , 1000000000000, count=count+1); count
time = 2,294 ms.
%196 = 37607912018
? 37607912018
%197 = 37607912018
? p2
%198 = 999781070909
? sumlogprimes=0; forprime(q=999781070910 , 1000000000000, sumlogprimes=sumlogprimes+log(q)); sumlogprimes
time = 1min, 25,717 ms.
%199 = 218964392.249194594870107709322349966327713173580
? 999999030333.09622463699607903975308725646673 – sumlogprimes
%200 = 999780065940.847030042125971330430737290139016826
? thetaCheb = 999999030333.09622463699607903975308725646673-sumlogprimes
%201 = 999780065940.847030042125971330430737290139016826
? thetaCheb
%202 = 999780065940.847030042125971330430737290139016826
? p
%203 = 3999819583387
? p=999781070909
%204 = 999781070909
? epsilon
%205 = 8.6159474458768635875553049472001443044 E-15
? epsilon=log(1+1/p)/log(p)
%206 = 3.61994187188332908418733101506308857973891597465 E-14
? \u
g =
(Y)->floor(log((exp((1+epsilon)*log(Y))-1)/(exp(epsilon*log(Y))-1))/log(Y))-1

? g(2)
%207 = 44
? g(17)
%208 = 10
? g(19)
%209 = 10
? prime(106913)
%210 = 1397251
? g(1397251)
%211 = 1
? prime(106912)
%212 = 1397233
? g(1397233)
%213 = 2
? sum=0; for(X=1,106912, sum = sum+(g(prime(X)-1)*log(prime(X)));sum
*** syntax error, unexpected $end, expecting )-> or ‘,’ or ‘)': …e(X)-1)*log(prime(X)));sum
*** ^-
? sum=0; for(X=1,106912, sum = sum+(g(prime(X))-1)*log(prime(X)))
*** variable name expected: sum=0;for(X=1,106912
*** ^——————–
? sum4=0; for(X=1,106912, sum4 = sum4+(g(prime(X))-1)*log(prime(X)))
time = 7,518 ms.
? sum4
%215 = 1412045.01159541398434404224867771016684988078484
? thetaCheb
%216 = 999780065940.847030042125971330430737290139016826
? thetaCheb+sum4
%217 = 999781477985.858625456110315372679415000305866707
? log(thetaCheb+sum4)
%218 = 27.6308025700349926529916290589321648678391771498
? 37599987401/80000000.0000
%219 = 469.999842512500000000000000000000000000000000000
? 469+1
%220 = 470
? 470*80000000
%221 = 37600000000

[david2@localhost eratosthenes7]$ time ./eratosthsiv3630a.out

size of int is: 4
size of long is: 8
size of char is: 1

pi(1000000000000) = 37607912018

sum_logs_primes = 999999030333.09622463699607903975308725646673
real 2365m37.094s
user 2364m50.247s
sys 0m2.488s

[david2@localhost eratosthenes7]$
—————————————

Number of big primes used in making current n is: 37598987400
numloops = 799999

number of steps: 17
44 27 18 15 12 11 10 10 9 8 8 8 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
record_low_variation_delta = -0.006989192976654998649573742516 record_low_log2n = 27.630802567271308507202087382619

current step number = 1 quotient de Robin: 0.999999972115669543306341175815
loglog n = 27.630802570008049110251729402793

sigma(n’)/n’ = 49.212458972117505944083146994669
record step is at: 1
log(log(n’)) = 27.630802570008049110251729402793 Robin upper bound = 49.212460344374012773540337008566 sigma(n’)/n’ = 49.212458972117505944083146994669
current step number = 2 quotient de Robin: 0.999999972115669796471084435642
loglog n = 27.630802570008454663982266449126

sigma(n’)/n’ = 49.212458972118240723486366399751
record step is at: 2
log(log(n’)) = 27.630802570008454663982266449126 Robin upper bound = 49.212460344374735094103809570873 sigma(n’)/n’ = 49.212458972118240723486366399751
current step number = 3 quotient de Robin: 0.999999972115664106313899496870
loglog n = 27.630802570008965601257088259561

sigma(n’)/n’ = 49.212458972118870713113682345841
record step is at: 2
log(log(n’)) = 27.630802570008965601257088259561 Robin upper bound = 49.212460344375645110391317775089 sigma(n’)/n’ = 49.212458972118870713113682345841
current step number = 4 quotient de Robin: 0.999999972115635775153723508512
loglog n = 27.630802570009302147036379714800

sigma(n’)/n’ = 49.212458972118075879405184158090
record step is at: 2
log(log(n’)) = 27.630802570009302147036379714800 Robin upper bound = 49.212460344376244522796204802772 sigma(n’)/n’ = 49.212458972118075879405184158090
current step number = 5 quotient de Robin: 0.999999972115619954714472491358
loglog n = 27.630802570009754230950421738977

sigma(n’)/n’ = 49.212458972118102510833377823037
record step is at: 2
log(log(n’)) = 27.630802570009754230950421738977 Robin upper bound = 49.212460344377049716986122103593 sigma(n’)/n’ = 49.212458972118102510833377823037
current step number = 6 quotient de Robin: 0.999999972115627194622094540962
loglog n = 27.630802570009921321548063048059

sigma(n’)/n’ = 49.212458972118756404946590923917
record step is at: 2
log(log(n’)) = 27.630802570009921321548063048059 Robin upper bound = 49.212460344377347317440886537232 sigma(n’)/n’ = 49.212458972118756404946590923917
current step number = 7 quotient de Robin: 0.999999972115605325383227100624
loglog n = 27.630802570010189644169063997968

sigma(n’)/n’ = 49.212458972118158067902126921320
record step is at: 2
log(log(n’)) = 27.630802570010189644169063997968 Robin upper bound = 49.212460344377825219460274166564 sigma(n’)/n’ = 49.212458972118158067902126921320
current step number = 8 quotient de Robin: 0.999999972115590010552154801447
loglog n = 27.630802570010491991110406975108

sigma(n’)/n’ = 49.212458972117942889168174424680
record step is at: 2
log(log(n’)) = 27.630802570010491991110406975108 Robin upper bound = 49.212460344378363721258163843418 sigma(n’)/n’ = 49.212458972117942889168174424680
current step number = 9 quotient de Robin: 0.999999972115625084463154265373
loglog n = 27.630802570010723843389296918164

sigma(n’)/n’ = 49.212458972120081908309822115148
record step is at: 2
log(log(n’)) = 27.630802570010723843389296918164 Robin upper bound = 49.212460344378776666957142892032 sigma(n’)/n’ = 49.212458972120081908309822115148
current step number = 10 quotient de Robin: 0.999999972115668176324314499768
loglog n = 27.630802570011070195311542746581

sigma(n’)/n’ = 49.212458972122819442656764330207
record step is at: 2
log(log(n’)) = 27.630802570011070195311542746581 Robin upper bound = 49.212460344379393544812772822695 sigma(n’)/n’ = 49.212458972122819442656764330207
current step number = 11 quotient de Robin: 0.999999972115634517989633902184
loglog n = 27.630802570011619423140264094097

sigma(n’)/n’ = 49.212458972122141247705688916999
record step is at: 2
log(log(n’)) = 27.630802570011619423140264094097 Robin upper bound = 49.212460344380371759349701059424 sigma(n’)/n’ = 49.212458972122141247705688916999
current step number = 12 quotient de Robin: 0.999999972115652463082734815002
loglog n = 27.630802570012276867855209347208

sigma(n’)/n’ = 49.212458972124195326503784859111
record step is at: 2
log(log(n’)) = 27.630802570012276867855209347208 Robin upper bound = 49.212460344381542715997843477838 sigma(n’)/n’ = 49.212458972124195326503784859111
current step number = 13 quotient de Robin: 0.999999972115666879890460152981
loglog n = 27.630802570013206414835827203974

sigma(n’)/n’ = 49.212458972126560403524500125030
record step is at: 2
log(log(n’)) = 27.630802570013206414835827203974 Robin upper bound = 49.212460344383198306486248011687 sigma(n’)/n’ = 49.212458972126560403524500125030
current step number = 14 quotient de Robin: 0.999999972115679079789989644612
loglog n = 27.630802570014600907757977282106

sigma(n’)/n’ = 49.212458972129644483407768658400
record step is at: 222
log(log(n’)) = 27.630802570014600907757977282106 Robin upper bound = 49.212460344385681999366972068265 sigma(n’)/n’ = 49.212458972129644483407768658400
current step number = 15 quotient de Robin: 0.999999972115680283018417941615
loglog n = 27.630802570016921922813175727773

sigma(n’)/n’ = 49.212458972133837593020364535794
record step is at: 1673
log(log(n’)) = 27.630802570016921922813175727773 Robin upper bound = 49.212460344389815895263526016736 sigma(n’)/n’ = 49.212458972133837593020364535794
current step number = 16 quotient de Robin: 0.999999972115680415057292588568
loglog n = 27.630802570021508921629356897342

sigma(n’)/n’ = 49.212458972142013867823292313363
record step is at: 106913
log(log(n’)) = 27.630802570021508921629356897342 Robin upper bound = 49.212460344397985672336379988117 sigma(n’)/n’ = 49.212458972142013867823292313363
current step number = 17
quotient de Robin: 0.999999972115680424387739328044
loglog n = 27.630802570034992652991629058932
sigma(n’)/n’ = 49.212458972166029828348808887298
record step is at: 37599987401
log(log(n’)) = 27.630802570034992652991629058932
PARI/GP
?
log(thetaCheb+sum4)
%218 = 27.6308025700349926529916290589321648678391771498

log(log(n’)) = 27.630802570034992652991629058932 30 digits OK .

Robin upper bound = 49.212460344422001174357312333199
sigma(n’)/n’ = 49.212458972166029828348808887298
=================================

Written by meditationatae

January 15, 2015 at 8:19 am

Posted in History

Program superabun3842a.out : Job Done

=================================
step at 1
step at 2
step at 3
step at 4
step at 5
step at 6
step at 7
step at 8
step at 9
step at 12
step at 16
step at 23
step at 40
step at 88
step at 299
step at 2527
step at 203099
step at 142959989401
/*** primes out to nearly 4e+12 included ***/
/*** job superabun3842a.out Done, around 7 am on January 6, 2015 (Epiphany) ***/
Number of big primes used in making current n is: 142958989400
numloops = 399999

number of steps: 18
46 29 19 16 13 12 11 10 9 9 9 8 8 8 8 7 7 7 7 7 7 7 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4
record_low_variation_delta = 0.003211974054498445404023465040
record_low_log2n = 29.017270659288498412335773035181
current step number = 1
quotient de Robin: 0.999999986589046437861233104296
loglog n = 29.017270660732345607599902625349
sigma(n’)/n’ = 51.681859726083558640077856393175
record step is at: 1
log(log(n’)) = 29.017270660732345607599902625349
Robin upper bound = 51.681860419186588726726782955098
sigma(n’)/n’ = 51.681859726083558640077856393175

current step number = 2
quotient de Robin: 0.999999986589042629639753070031
loglog n = 29.017270660732446978419894572458
sigma(n’)/n’ = 51.681859726083542372875935288624
record step is at: 1
log(log(n’)) = 29.017270660732446978419894572458
Robin upper bound = 51.681860419186769275498259661439
sigma(n’)/n’ = 51.681859726083542372875935288624
current step number = 3
quotient de Robin: 0.999999986589043379045163364120
loglog n = 29.017270660732574690549294956045
sigma(n’)/n’ = 51.681859726083808568089814792108
record step is at: 1
log(log(n’)) = 29.017270660732574690549294956045
Robin upper bound = 51.681860419186996740049377479687
sigma(n’)/n’ = 51.681859726083808568089814792108

current step number = 4
quotient de Robin: 0.999999986589035775978634752919
loglog n = 29.017270660732658812378396241635
sigma(n’)/n’ = 51.681859726083565454534279174898
record step is at: 1
log(log(n’)) = 29.017270660732658812378396241635
Robin upper bound = 51.681860419187146567118940664617
sigma(n’)/n’ = 51.681859726083565454534279174898

current step number = 5
quotient de Robin: 0.999999986589030591052678243773
loglog n = 29.017270660732771813723522486277
sigma(n’)/n’ = 51.681859726083498751491012054497
record step is at: 1
log(log(n’)) = 29.017270660732771813723522486277
Robin upper bound = 51.681860419187347830697940810036
sigma(n’)/n’ = 51.681859726083498751491012054497

current step number = 6
quotient de Robin: 0.999999986589029805518138999609
loglog n = 29.017270660732813579116417366573
sigma(n’)/n’ = 51.681859726083532540792914377657
record step is at: 1
log(log(n’)) = 29.017270660732813579116417366573
Robin upper bound = 51.681860419187422217887252405119
sigma(n’)/n’ = 51.681859726083532540792914377657

current step number = 7
quotient de Robin: 0.999999986589026061870345749887
loglog n = 29.017270660732880648118784259794
sigma(n’)/n’ = 51.681859726083458516858820834806
record step is at: 1
log(log(n’)) = 29.017270660732880648118784259794
Robin upper bound = 51.681860419187541672637470197940
sigma(n’)/n’ = 51.681859726083458516858820834806

current step number = 8
quotient de Robin: 0.999999986589031620739508139281
loglog n = 29.017270660732908455773770530849
sigma(n’)/n’ = 51.681859726083795337005600793366
record step is at: 1
log(log(n’)) = 29.017270660732908455773770530849
Robin upper bound = 51.681860419187591200084775232915
sigma(n’)/n’ = 51.681859726083795337005600793366

current step number = 9
quotient de Robin: 0.999999986589044931624163601610
loglog n = 29.017270660732956221723607118211
sigma(n’)/n’ = 51.681859726084568342903052420668
record step is at: 1
log(log(n’)) = 29.017270660732956221723607118211
Robin upper bound = 51.681860419187676274700548282070
sigma(n’)/n’ = 51.681859726084568342903052420668

current step number = 10
quotient de Robin: 0.999999986589025232406927179554
loglog n = 29.017270660733075082974589837780
sigma(n’)/n’ = 51.681859726083761951200326422131
record step is at: 1
log(log(n’)) = 29.017270660733075082974589837780
Robin upper bound = 51.681860419187887975196241414208
sigma(n’)/n’ = 51.681859726083761951200326422131

current step number = 11
quotient de Robin: 0.999999986589030408154107397324
loglog n = 29.017270660733164930501361674424
sigma(n’)/n’ = 51.681859726084189468393271306590
record step is at: 1
log(log(n’)) = 29.017270660733164930501361674424
Robin upper bound = 51.681860419188048000147999368347
sigma(n’)/n’ = 51.681859726084189468393271306590

current step number = 12
quotient de Robin: 0.999999986589047192132098084605
loglog n = 29.017270660733277072700610326954
sigma(n’)/n’ = 51.681859726085256628976360652147
record step is at: 23
log(log(n’)) = 29.017270660733277072700610326954
Robin upper bound = 51.681860419188247733525973904474
sigma(n’)/n’ = 51.681859726085256628976360652147

current step number = 13
quotient de Robin: 0.999999986589041542424690020430
loglog n = 29.017270660733460693676316724116
sigma(n’)/n’ = 51.681859726085291683837496987711
record step is at: 23
log(log(n’)) = 29.017270660733460693676316724116
Robin upper bound = 51.681860419188574775781169016669
sigma(n’)/n’ = 51.681859726085291683837496987711

current step number = 14
quotient de Robin: 0.999999986589046144656521894876
loglog n = 29.017270660733703552509209863633
sigma(n’)/n’ = 51.681859726085962084903579033867
record step is at: 23
log(log(n’)) = 29.017270660733703552509209863633
Robin upper bound = 51.681860419189007324949900278098
sigma(n’)/n’ = 51.681859726085962084903579033867
current step number = 15
quotient de Robin: 0.999999986589048621691309083751
loglog n = 29.017270660734069984819664656743
sigma(n’)/n’ = 51.681859726086742745142162901531
record step is at: 299
log(log(n’)) = 29.017270660734069984819664656743
Robin upper bound = 51.681860419189659967431111731368
sigma(n’)/n’ = 51.681859726086742745142162901531

current step number = 16
quotient de Robin: 0.999999986589048854745104176337
loglog n = 29.017270660734679083869566111649
sigma(n’)/n’ = 51.681859726087839639298925691649
record step is at: 2527
log(log(n’)) = 29.017270660734679083869566111649
Robin upper bound = 51.681860419190744816948715247920
sigma(n’)/n’ = 51.681859726087839639298925691649

current step number = 17
quotient de Robin: 0.999999986589048856456665384413
loglog n = 29.017270660735883427605857650256
sigma(n’)/n’ = 51.681859726089984751137314462242
record step is at: 203099
log(log(n’)) = 29.017270660735883427605857650256
Robin upper bound = 51.681860419192889840359203367946
sigma(n’)/n’ = 51.681859726089984751137314462242

current step number = 18
quotient de Robin: 0.999999986589048857340123754459
loglog n = 29.017270660739426955750532798263
sigma(n’)/n’ = 51.681859726096296076952299244106
record step is at: 142959989401
log(log(n’)) = 29.017270660739426955750532798263
Robin upper bound = 51.681860419199201120600056253916
sigma(n’)/n’ = 51.681859726096296076952299244106
=================================

Written by meditationatae

January 6, 2015 at 7:26 pm

Posted in History

Eratosthenes sieving is taking time at this point cmp. to rest of work

=================================
step at 1
step at 2
step at 3
step at 4
step at 5
step at 6
step at 7
step at 9
step at 12
step at 16
step at 23
step at 39
step at 86
step at 293
step at 2426
step at 190492
step at 125119987201

Number of big primes used in making current n is: 125118987200
numloops = 399999

number of steps: 17
46 28 19 16 13 12 10 10 9 9 9 8 8 8 8 7 7 7 7 7 7 7 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4
record_low_variation_delta = -0.007368469666027751124259883644
record_low_log2n = 28.879017934136522792132536896267
current step number = 1
quotient de Robin: 0.999999985712376696215687414006
loglog n = 28.879017935786544805445185194995
sigma(n’)/n’ = 51.435621569180841652007091728883
record step is at: 1
log(log(n’)) = 28.879017935786544805445185194995
Robin upper bound = 51.435622304073637528337753048246
sigma(n’)/n’ = 51.435621569180841652007091728883
current step number = 2
quotient de Robin: 0.999999985712378826743462622102
loglog n = 28.879017935786661206081674807056
sigma(n’)/n’ = 51.435621569181158554989171741704
record step is at: 2
log(log(n’)) = 28.879017935786661206081674807056
Robin upper bound = 51.435622304073844846300841199670
sigma(n’)/n’ = 51.435621569181158554989171741704
current step number = 3
quotient de Robin: 0.999999985712372423486781711921
loglog n = 28.879017935786807853540488191721
sigma(n’)/n’ = 51.435621569181090389237345499325
record step is at: 2
log(log(n’)) = 28.879017935786807853540488191721
Robin upper bound = 51.435622304074106036044902072666
sigma(n’)/n’ = 51.435621569181090389237345499325
current step number = 4
quotient de Robin: 0.999999985712364374657846513268
loglog n = 28.879017935786904447752223260608
sigma(n’)/n’ = 51.435621569180848433996045291561
record step is at: 2
log(log(n’)) = 28.879017935786904447752223260608
Robin upper bound = 51.435622304074278077331160908966
sigma(n’)/n’ = 51.435621569180848433996045291561
current step number = 5
quotient de Robin: 0.999999985712358590936637213522
loglog n = 28.879017935787034203321902202569
sigma(n’)/n’ = 51.435621569180782048759345522845
record step is at: 2
log(log(n’)) = 28.879017935787034203321902202569
Robin upper bound = 51.435622304074509181397396677743
sigma(n’)/n’ = 51.435621569180782048759345522845
current step number = 6
quotient de Robin: 0.999999985712357584086864239433
loglog n = 28.879017935787082161090386157820
sigma(n’)/n’ = 51.435621569180815677072160619750
record step is at: 2
log(log(n’)) = 28.879017935787082161090386157820
Robin upper bound = 51.435622304074594597656071810032
sigma(n’)/n’ = 51.435621569180815677072160619750
current step number = 7
quotient de Robin: 0.999999985712379331673053735588
loglog n = 28.879017935787159174125940662799
sigma(n’)/n’ = 51.435621569182071443492920907250
record step is at: 7
log(log(n’)) = 28.879017935787159174125940662799
Robin upper bound = 51.435622304074731763449523637303
sigma(n’)/n’ = 51.435621569182071443492920907250
current step number = 8
quotient de Robin: 0.999999985712371954328274289226
loglog n = 28.879017935787245952704863998656
sigma(n’)/n’ = 51.435621569181846544104422825170
record step is at: 7
log(log(n’)) = 28.879017935787245952704863998656
Robin upper bound = 51.435622304074886322382916376330
sigma(n’)/n’ = 51.435621569181846544104422825170
current step number = 9
quotient de Robin: 0.999999985712351625264098094575
loglog n = 28.879017935787382437003495872281
sigma(n’)/n’ = 51.435621569181043994453969583358
record step is at: 7
log(log(n’)) = 28.879017935787382437003495872281
Robin upper bound = 51.435622304075129410802698343757
sigma(n’)/n’ = 51.435621569181043994453969583358
current step number = 10
quotient de Robin: 0.999999985712356324908331334524
loglog n = 28.879017935787485605837526108301
sigma(n’)/n’ = 51.435621569181469474741776128882
record step is at: 7
log(log(n’)) = 28.879017935787485605837526108301
Robin upper bound = 51.435622304075313161967385805648
sigma(n’)/n’ = 51.435621569181469474741776128882
current step number = 11
quotient de Robin: 0.999999985712372514643672565007
loglog n = 28.879017935787614374879454775908
sigma(n’)/n’ = 51.435621569182531550839583948710
record step is at: 7
log(log(n’)) = 28.879017935787614374879454775908
Robin upper bound = 51.435622304075542508956255978852
sigma(n’)/n’ = 51.435621569182531550839583948710
current step number = 12
quotient de Robin: 0.999999985712374981156195126455
loglog n = 28.879017935787815087286993769050
sigma(n’)/n’ = 51.435621569183015900774011212733
record step is at: 7
log(log(n’)) = 28.879017935787815087286993769050
Robin upper bound = 51.435622304075899992289272087410
sigma(n’)/n’ = 51.435621569183015900774011212733
current step number = 13
quotient de Robin: 0.999999985712377938211188484148
loglog n = 28.879017935788095154942979248848
sigma(n’)/n’ = 51.435621569183666819507901883372
record step is at: 7
log(log(n’)) = 28.879017935788095154942979248848
Robin upper bound = 51.435622304076398813066518992860
sigma(n’)/n’ = 51.435621569183666819507901883372
current step number = 14
quotient de Robin: 0.999999985712379547227670397820
loglog n = 28.879017935788515111240323397466
sigma(n’)/n’ = 51.435621569184497552839220833846
record step is at: 293
log(log(n’)) = 28.879017935788515111240323397466
Robin upper bound = 51.435622304077146785644479946198
sigma(n’)/n’ = 51.435621569184497552839220833846
current step number = 15
quotient de Robin: 0.999999985712380030893945211680
loglog n = 28.879017935789211010657252409982
sigma(n’)/n’ = 51.435621569185761877754532353364
record step is at: 2426
log(log(n’)) = 28.879017935789211010657252409982
Robin upper bound = 51.435622304078386232901667671439
sigma(n’)/n’ = 51.435621569185761877754532353364
current step number = 16
quotient de Robin: 0.999999985712380033437882384204
loglog n = 28.879017935790587302652786331406
sigma(n’)/n’ = 51.435621569188213284280847185000
record step is at: 190492
log(log(n’)) = 28.879017935790587302652786331406
Robin upper bound = 51.435622304080837508614013827635
sigma(n’)/n’ = 51.435621569188213284280847185000
current step number = 17
quotient de Robin: 0.999999985712380033999426435424
loglog n = 28.879017935794636385201502681326
sigma(n’)/n’ = 51.435621569195425022306860892615
record step is at: 125119987201
log(log(n’)) = 28.879017935794636385201502681326
Robin upper bound = 51.435622304088049217859697970617
sigma(n’)/n’ = 51.435621569195425022306860892615
done.
=================================

Written by meditationatae

January 5, 2015 at 12:51 am

Posted in History

Source code for $HOME//eratosthenes6/superabun3842a.c

#include <stdio.h>
#include <quadmath.h>
#include <stdlib.h>
__float128 splogs[250000];
__float128 theta[250000];
__float128 prod100k[250000];
long ptr_exponents[250000];
long ptr_current_powers[250000];
long ptr_current_sigmas[250000];
long pts_primes[250000];
long ptr_isstep[250000];
long sivsmall_primes[150000];

unsigned char sivptr_remains[10000000];

int main(void)
{
long theIndex;
__float128 euler = 0.5772156649015328606065120900824024Q;
long j;
long numprimes;
long num_new_primes;
long file_offset;
long jj;
long kij;
long kijj;
long numBigPrimesUsed;
__float128 sum_log_cofactor;
__float128 sum_theta_Cheb;
long numsteps;
long expon;
long sigma;
long * ptr_primes;
long list_steps[1000];
long power;
long old_prime;
long powerb;
int nownow;
int go_skip;
int answer;
long k;
long l;
long numloops;
long vintageloops;
long tmp_exponent;
long m;
long p;
long sum;
int not_done;
int junk;
int leave_loop;
long ljunk;
int skip_base_case;
long current_step;
long now_step;
__float128 RecordRobinQuotient;
__float128 RecordQuotient;
__float128 tmp_now_n;
__float128 log2nprime;
__float128 robin_bound;
__float128 base_tmp_now_n;
long RecordStep;
__float128 tmp_now_robin;
__float128 constant;
__float128 prod_sigma_r;
__float128 prod_sigma_rone;
__float128 base_tmp_now_sigma_r;
__float128 prod_sigma_r_cofactor;
__float128 tmp_now_sigma_r;
__float128 tmp_now_quotient;
__float128 delta;
__float128 delta_log;
__float128 delta_estimate;
__float128 variation_delta;
__float128 record_low_variation_delta;
__float128 record_low_log2n;
__float128 tmp_el_now_robin;
__float128 now_n;
long current_step_number;
__float128 sum_logs_primes;
__float128 sum_logs_all;
__float128 ratio;
__float128 now_robin;
__float128 val128a;
FILE *in;
long sivoffset;
long sivj;
long sivp;
long sivblock_size;
unsigned char sivuc1;
unsigned char sivuc0;
long sivindex;
long sivblockprimecount;
long sivrem;
long sivcount;
long sivcount_new_primes;
long sivbarred;
long siv_left_overs;
long siv_keeps;
long sivp_num;
long siv_last_sivj;
long sivoffset_next;
int sivbatchdone;
FILE *out;
ptr_primes = (long *) calloc(80000000, sizeof(long));

sivblock_size = (long) 10000000;
sivuc1 = (unsigned char) 1;
sivuc0 = (unsigned char) 0;

sivcount = 8000000000 ;
sivoffset = 199815106450;

record_low_variation_delta = (__float128) 100;
record_low_log2n = (__float128) 0;
in = fopen(“/home/david2/eratosthenes/primes100meg01a_tmp.txt”, “r”);
for(j=0; j< 250000 ; j++)
{
fscanf(in, “%ld”, &theIndex);
fscanf(in, “%ld”, &pts_primes[j]);
}
fclose(in);

for(sivj=0; sivj< 150000; sivj++)
{
sivsmall_primes[sivj] = pts_primes[sivj] ;
}
constant = ((__float128) 323336)/((__float128) 1000000);

val128a = 1.0Q;
for(j=0; j<250000; j++)
{
val128a = val128a*(1.0Q + 1.0Q/((__float128)pts_primes[j]));
prod100k[j] = val128a;
}
in = fopen(“/home/david2/eratosthenes/LargePrimes_to_1e10a.txt”, “r”);
for(j=0; j<79920000 ; j++)
{
fscanf(in, “%ld”, &ljunk);
}
for(j=0; j< 80000000 ; j++)
{
fscanf(in, “%ld”, &ptr_primes[j]);
}

fclose(in);

for(j=0; j< 250000 ; j++)
{
ptr_exponents[j] = (long) 0;
}
prod_sigma_r = (__float128) 1;

prod_sigma_rone = (__float128) 1;

for(j=0; j< 250000 ; j++)
{
ptr_isstep[j] = (long) 0;
}
in = fopen(“/home/david2/eratosthenes/exponents_out802a.txt”, “r”);
for(j=0; j< 250000 ; j++)
{
fscanf(in, “%ld”, &theIndex);
fscanf(in, “%ld”, &ptr_exponents[j]);
}
fclose(in);

for(j=0; j< 250000 ; j++)
{
p = pts_primes[j];
power = (long) 1;

for(l=0; l<ptr_exponents[j]; l++)
{
power = power*p;
}

ptr_current_powers[j] = power;
}
for(j=0; j< 250000 ; j++)
{
p = pts_primes[j];
power = (long) 1;

for(l=0; l<ptr_exponents[j]; l++)
{
power = power*p + ((long) 1);
}

ptr_current_sigmas[j] = power;
}
numprimes = (long) 80000000;

numBigPrimesUsed = (long) 79000000;

leave_loop = 0;
in = fopen(“/home/david2/eratosthenes/primes_out802a.txt”, “r”);

sum_logs_primes = (__float128) 0;
sum_logs_all = (__float128) 0;
for(j=0; j<80000000; j++)
{
fscanf(in, “%ld”, &ljunk);
fscanf(in, “%ld”, &old_prime);
sum_logs_primes = sum_logs_primes + logq((__float128)old_prime);

if(j < 250000)
{
sum_logs_all = sum_logs_all + ((__float128)ptr_exponents[j])*logq((__float128)old_prime);
}
else
{
sum_logs_all = sum_logs_all + logq((__float128)old_prime);
}
}

fclose(in);

for(j=0; j<250000; j++)
{
splogs[j] = logq((__float128) pts_primes[j]);
}

sum_theta_Cheb = (__float128) 0;
for(j=0; j<250000; j++)
{
sum_theta_Cheb = sum_theta_Cheb + logq((__float128) pts_primes[j]) ;
theta[j] = sum_theta_Cheb;
}
skip_base_case = (int) 0;
for(j=0; j< 250000 ; j++)
{

p = pts_primes[j];

expon = ptr_exponents[j];

ratio = (__float128) 1;

for(jj = 0; jj < 1; jj++)
{
ratio = ((__float128)1) + (ratio/((__float128) p) );
}

if(expon == 1)
{
prod_sigma_rone = prod_sigma_rone*ratio;
}
prod_sigma_r = prod_sigma_r*ratio;
}

in = fopen(“/home/david2/eratosthenes/primes_out802a.txt”, “r”);

for(j=0 ; j<numprimes; j++)
{
fscanf(in, “%ld”, &ljunk);
fscanf(in, “%ld”, &old_prime);

if( j > 249999 )
{
prod_sigma_r = prod_sigma_r + (prod_sigma_r/((__float128)old_prime)) ;
prod_sigma_rone = prod_sigma_rone + (prod_sigma_rone/((__float128)old_prime)) ;
}
}

fclose(in);
for(numloops = 0; numloops < 80002284 ; numloops++)
{

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;
if( (2283 ==(numloops%64000)) || (((numloops – 80002283) < 6)&&((80002283-numloops) < 6)) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);

if(numloops == 80002283)
{
printf(“numloops = %ld\n”, numloops);
printf(“break from current loop, ok?\n”);
printf(“enter 1 for yes, 0 for no:\n”);

if(1 == 1)
{
leave_loop = 1;
}
else
{
leave_loop = 1;
}
}
}

if(leave_loop == 0)
{
if((2283 ==(numloops%64000)) || (((numloops – 80002283) < 6)&&((80002283-numloops) < 6)) )
{
printf(“number of steps: %ld\n”, numsteps);
}
RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];
// p = pts_primes[j];
// power = (long) 1;
// for(l=0; l<ptr_exponents[j]+((long)1); l++)
// {
// power = power*p;
// }

// powerb = power/p;

powerb = ptr_current_powers[j];

// sigma = (power – ((long)1) )/(p – ((long)1));

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}
}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];
for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{
p = pts_primes[list_steps[j]];

if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}
tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if((2283 ==(numloops%64000)) || (((numloops – 80002283) < 6)&&((80002283-numloops) < 6)) )
{

printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep);

}
}
else
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{
tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step-80000000]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step-80000000] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if((2283 ==(numloops%64000)) || (((numloops – 80002283) < 6)&&((80002283-numloops) < 6)) )
{
printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep);
}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;
p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;
ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);

}
if(RecordStep == numprimes)
{
sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes-80000000]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-80000000]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 2283 ==(numloops%64000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n\n”);
}
}
/*** if leave loop == 0 ****/
if( leave_loop == 1 )
{
break;
}
}

/**************** next 80 million batch … *****************/
/*************************************************************
prime 160,000,000 is:

3340200037

or

3,340,200,037 .

:159920000p
3340200037
3340200037
************************************************************/

in = fopen(“/home/david2/eratosthenes/LargePrimes_to_1e11ofNov22a.txt”, “r”);
for(j=0; j< 159920000 ; j++)
{
fscanf(in, “%ld”, &old_prime);
}
for(j=0; j< 80000000 ; j++)
{
fscanf(in, “%ld”, &ptr_primes[j]);
}
/**************************************

==============================================
next: loops ….

******************************************************/
file_offset = (long) 160000000;
num_new_primes = (long) 0;

numloops = (long) 0;
while( num_new_primes < ((long)80000000) )
{
numloops++;

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;

if( 9999 == (num_new_primes%10000) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);
}
if( 9999 == (num_new_primes%10000) )
{
printf(“number of steps: %ld\n”, numsteps);
}
RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];

powerb = ptr_current_powers[j];

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}
}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];

for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{
if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}
tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];
ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}

tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if( 9999 == (num_new_primes%10000) )
{

printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep);

}
}
else
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{

tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step- file_offset]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step- file_offset] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if( 9999 == (num_new_primes%10000) )
{
printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep);
}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;

p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;

ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);

}
if(RecordStep == numprimes)
{
sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 99999 == (num_new_primes%100000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n\n”);
}
}
/********************** Next batch 80 M and loop *******************/

for(kij = 1; kij < 49; kij++)
{

for(j=0; j< 80000000 ; j++)
{
fscanf(in, “%ld”, &ptr_primes[j]);
}

file_offset = file_offset + ((long)80000000) ;

/*** 240 000 000 for kij=1 ***/
num_new_primes = (long) 0;

numloops = (long) 0;

while( num_new_primes < ((long)80000000) )
{
numloops++;

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;

if( 99999 == (numloops%100000) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);
}
if( 99999 == (numloops%100000) )
{
printf(“number of steps: %ld\n”, numsteps);
}
if( 99999 == (numloops%100000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n”);
}

RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];

powerb = ptr_current_powers[j];

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}
}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];

for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{
p = pts_primes[list_steps[j]];

if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}

tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

log2nprime = logq(tmp_now_n);

robin_bound = expq(euler)*log2nprime;

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if( 99999 == (numloops%100000) )
{

printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);
}
}
else
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{

tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step- file_offset]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step- file_offset] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);
log2nprime = logq(tmp_now_n);
robin_bound = expq(euler)*log2nprime;
tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if( 99999 == (numloops%100000) )
{
printf(“current step number = %ld “, current_step_number);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);

}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;

p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;

ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);

}
if(RecordStep == numprimes)
{

if(num_new_primes < 79999500)
{

for(j=0; j< 100 ; j++)
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
}
else
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 99999 == (numloops%100000) )
{
printf(“=================================\n”);
}
}
}

fclose(in);
/********************** Next batch 80 M and loop *******************/

/*****************************************************************
? primepi(99036319010)

%37 = 4080000000

4,080,000,000 primes included in `n’
in = fopen(“/home/david2/eratosthenes/LargePrimes_to_1e11ofNov22a.txt”, “r”);
**********************************************************************/
in = fopen(“/home/david2/eratosthenes2/LargePrimes_to_2e11ofNov26a.txt”, “r”);
for(kij = 1; kij < 50; kij++)
{

for(j=0; j< 80000000 ; j++)
{
fscanf(in, “%ld”, &ptr_primes[j]);
}

file_offset = file_offset + ((long)80000000) ;
num_new_primes = (long) 0;

numloops = (long) 0;

while( num_new_primes < ((long)80000000) )
{
numloops++;

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;

if( 99999 == (numloops%100000) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]+1);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);
}
if( 99999 == (numloops%100000) )
{
printf(“number of steps: %ld\n”, numsteps);
}
if( 99999 == (numloops%100000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n”);
}

if( 799999 == (numloops%800000) )
{
printf(“record_low_variation_delta = %.30Qf “, record_low_variation_delta);
printf(“record_low_log2n = %.30Qf\n\n”, record_low_log2n);
fflush(stdout);

record_low_variation_delta = (__float128) 100;
record_low_log2n = (__float128) 0;
}

RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];

powerb = ptr_current_powers[j];

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}
}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];

for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{
p = pts_primes[list_steps[j]];

if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}

tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

log2nprime = logq(tmp_now_n);

robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if( 99999 == (numloops%100000) )
{

printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);
}
}
else
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{

tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step- file_offset]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step- file_offset] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);
log2nprime = logq(tmp_now_n);
robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if( 99999 == (numloops%100000) )
{
printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);

}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;
p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;

ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);

}
if(RecordStep == numprimes)
{

if(num_new_primes < 79999500)
{

for(j=0; j< 100 ; j++)
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
}
else
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 99999 == (numloops%100000) )
{
printf(“=================================\n”);
}
}
}

fclose(in);
/*****************************************************************
? primepi(99036319010)

%37 = 4080000000

4,080,000,000 primes included in `n’
in = fopen(“/home/david2/eratosthenes/LargePrimes_to_1e11ofNov22a.txt”, “r”);
Now, after another 49 batches of 80,000,000

we have done:

3,920,000,000 + 4,080,000,000 =

8,000,000,000 primes included in `n’

37,607,912,018 primes below 10^12 .

370 batches of 80 million

**********************************************************************/
for(kijj = 1; kijj <= 370 ; kijj++)
{

sivcount_new_primes = (long) 0;
sivbatchdone = 0;

while( (sivcount_new_primes < 80000000) && (sivbatchdone == 0) )
{

sivblockprimecount = (long) 0;

for(sivj=0; sivj< sivblock_size; sivj++)
{
sivptr_remains[sivj] = sivuc1;
}

for(sivj=0; sivj< 78498; sivj++)
{
sivp = sivsmall_primes[sivj];
sivrem = sivoffset%sivp;

if(sivrem == 0)
{
sivbarred = sivoffset;
}
else
{
sivbarred = sivoffset + sivp – sivrem;
}

sivindex = sivbarred – sivoffset;

while(sivindex< sivblock_size)
{
sivptr_remains[sivindex] = sivuc0;
sivindex = sivindex+sivp;
}
}

for(sivj=0; sivj< sivblock_size; sivj++)
{
if( sivptr_remains[sivj] == sivuc1 )
{
sivcount++;
sivcount_new_primes++;
sivblockprimecount++;
if(sivcount_new_primes <= 80000000)
{
ptr_primes[sivcount_new_primes – 1] = sivoffset + sivj ;
}
}
}

if(sivcount_new_primes >= 80000000 )
{
sivbatchdone = 1;
siv_left_overs = sivcount_new_primes – 80000000;
siv_keeps = sivblockprimecount – siv_left_overs;
sivp_num = (long) 0;

for(sivj=0; sivj< sivblock_size; sivj++)
{
if(sivptr_remains[sivj] == sivuc1 )
{
sivp_num++;
if(sivp_num == siv_keeps)
{
siv_last_sivj = sivj;
}
}
}
sivoffset_next = sivoffset + siv_last_sivj + ((long) 1);
sivoffset = sivoffset_next;
}
else
{
sivoffset = sivoffset + sivblock_size;
}
}
if( kijj == 1 )
{

out=fopen(“/home/david2/eratosthenes6/batchp001a.txt”, “w”);

for(j=0; j< 80000000 ; j++)
{
fprintf(out, “%ld\n”, ptr_primes[j]);
}

fclose(out);
}
file_offset = file_offset + ((long)80000000) ;
num_new_primes = (long) 0;

numloops = (long) 0;
while( num_new_primes < ((long)80000000) )
{
numloops++;

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;

if( 99999 == (numloops%100000) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]+1);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);
}
if( 99999 == (numloops%100000) )
{
printf(“number of steps: %ld\n”, numsteps);
}
if( 99999 == (numloops%100000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n”);
}

if( 799999 == (numloops%800000) )
{
printf(“\n\nrecord_low_variation_delta = %.30Qf “, record_low_variation_delta);
printf(“record_low_log2n = %.30Qf\n\n”, record_low_log2n);
fflush(stdout);
record_low_variation_delta = (__float128) 100;
record_low_log2n = (__float128) 0;
}

RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];

powerb = ptr_current_powers[j];

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}

}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];

for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{
p = pts_primes[list_steps[j]];

if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}

tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

log2nprime = logq(tmp_now_n);

robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if( 99999 == (numloops%100000) )
{

printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);
}
}
else
{
for(j=0; j<= numsteps- ((long)2) ; j++)
{

tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step- file_offset]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step- file_offset] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);
log2nprime = logq(tmp_now_n);
robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if( 99999 == (numloops%100000) )
{
printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);

}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;

p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;

ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);
}
if(RecordStep == numprimes)
{

if(num_new_primes < 79999500)
{

for(j=0; j< 100 ; j++)
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
}
else
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 99999 == (numloops%100000) )
{
printf(“=================================\n”);
}
}

}
/*****************************************************************
? primepi(99036319010)

%37 = 4080000000

4,080,000,000 primes included in `n’
in = fopen(“/home/david2/eratosthenes/LargePrimes_to_1e11ofNov22a.txt”, “r”);
Now, after another 49 batches of 80,000,000

we have done:

3,920,000,000 + 4,080,000,000 =

8,000,000,000 primes included in `n’

37,607,912,018 primes below 10^12 .

370 batches of 80 million
above is done already.
Now,
470 batches of 80 million have been completed.
about 37,600,000,000 primes included in `n’ ,

i.e. below just under 10^12.

Next, go to 4*10^12
Nicely:

pi(4e+12) ~= 142,966,208,126

1787 bacthes in all.

470 batches are done.

1317 batches remain to be done.

Use sieving for first 150,000 primes to cover
numbers below 4e+12 for primality testing.

9 December 2014

6:15 pm
**********************************************************************/
for(kijj = 1; kijj <= 1317 ; kijj++)
{

sivcount_new_primes = (long) 0;
sivbatchdone = 0;

while( (sivcount_new_primes < 80000000) && (sivbatchdone == 0) )
{

sivblockprimecount = (long) 0;

for(sivj=0; sivj< sivblock_size; sivj++)
{
sivptr_remains[sivj] = sivuc1;
}

for(sivj=0; sivj< 150000 ; sivj++)
{
sivp = sivsmall_primes[sivj];
sivrem = sivoffset%sivp;

if(sivrem == 0)
{
sivbarred = sivoffset;
}
else
{
sivbarred = sivoffset + sivp – sivrem;
}

sivindex = sivbarred – sivoffset;

while(sivindex< sivblock_size)
{
sivptr_remains[sivindex] = sivuc0;
sivindex = sivindex+sivp;
}
}

for(sivj=0; sivj< sivblock_size; sivj++)
{
if( sivptr_remains[sivj] == sivuc1 )
{
sivcount++;
sivcount_new_primes++;
sivblockprimecount++;
if(sivcount_new_primes <= 80000000)
{
ptr_primes[sivcount_new_primes – 1] = sivoffset + sivj ;
}
}
}

if(sivcount_new_primes >= 80000000 )
{
sivbatchdone = 1;
siv_left_overs = sivcount_new_primes – 80000000;
siv_keeps = sivblockprimecount – siv_left_overs;
sivp_num = (long) 0;

for(sivj=0; sivj< sivblock_size; sivj++)
{
if(sivptr_remains[sivj] == sivuc1 )
{
sivp_num++;
if(sivp_num == siv_keeps)
{
siv_last_sivj = sivj;
}
}
}
sivoffset_next = sivoffset + siv_last_sivj + ((long) 1);
sivoffset = sivoffset_next;
}
else
{
sivoffset = sivoffset + sivblock_size;
}
}
if( kijj == 1 )
{

out=fopen(“/home/david2/eratosthenes6/batchp002a.txt”, “w”);

for(j=0; j< 80000000 ; j++)
{
fprintf(out, “%ld\n”, ptr_primes[j]);
}

fclose(out);
}
file_offset = file_offset + ((long)80000000) ;
num_new_primes = (long) 0;

numloops = (long) 0;
while( num_new_primes < ((long)80000000) )
{
numloops++;

ptr_isstep[0] = (long) 1;
list_steps[0] = (long) 0;
numsteps = (long) 1;
not_done = (int) 1;
j = (long) 0;

while(not_done == 1)
{
j++;

if(ptr_exponents[j]< ptr_exponents[j-1])
{
ptr_isstep[j] = (long) 1;
list_steps[numsteps] = j;
numsteps++;
}
else
{
ptr_isstep[j] = (long) 0;
}

if(ptr_exponents[j] == ((long) 1))
{
not_done = (int) 0;
}

}

list_steps[numsteps] = numprimes;
numsteps++;

if( 99999 == (numloops%100000) )
{
for(j=0; j< numsteps; j++)
{
printf(“step at %ld\n”, list_steps[j]+1);
}
printf(“\nNumber of big primes used in making current n is: %ld\n”, numBigPrimesUsed);
printf(“numloops = %ld\n”, numloops);
printf(“\n”);
}
if( 99999 == (numloops%100000) )
{
printf(“number of steps: %ld\n”, numsteps);
}
if( 99999 == (numloops%100000) )
{
for(j=0; j< 200 ; j++)
{
printf(“%ld “, ptr_exponents[j]);
}

printf(“\n”);
}

if( 399999 == (numloops%400000) )
{
printf(“\n\nrecord_low_variation_delta = %.30Qf “, record_low_variation_delta);
printf(“record_low_log2n = %.30Qf\n\n”, record_low_log2n);
fflush(stdout);
record_low_variation_delta = (__float128) 100;
record_low_log2n = (__float128) 0;
}

RecordRobinQuotient = (__float128) 0;
if(skip_base_case == 0)
{

base_tmp_now_n = (__float128) 0;

base_tmp_now_sigma_r = (__float128) 1;

now_step = (long) 0;

for(j=0; j<= list_steps[numsteps-2]; j++)
{
if(j == list_steps[now_step] )
{
now_step++;
}
else
{
base_tmp_now_n = base_tmp_now_n + ((__float128)ptr_exponents[j])*splogs[j];

powerb = ptr_current_powers[j];

sigma = ptr_current_sigmas[j];

ratio = ((__float128)sigma)/((__float128)powerb);
base_tmp_now_sigma_r = base_tmp_now_sigma_r*ratio;
}
}
}

sum_log_cofactor = sum_logs_primes;

prod_sigma_r_cofactor = prod_sigma_r;
sum_log_cofactor = sum_log_cofactor – theta[list_steps[numsteps-2]];

prod_sigma_r_cofactor = prod_sigma_r_cofactor/prod100k[list_steps[numsteps-2]];

for(m=0; m< numsteps ; m++)
{
current_step_number = m;

current_step = list_steps[m];

tmp_now_n = sum_log_cofactor + base_tmp_now_n;
tmp_now_sigma_r = base_tmp_now_sigma_r*prod_sigma_r_cofactor;
if(m < numsteps-((long)1) )
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{
p = pts_primes[list_steps[j]];

if(j == m)
{
tmp_exponent = ptr_exponents[list_steps[j]] + ((long)1);
powerb = ptr_current_powers[list_steps[j]]*p;
sigma = ptr_current_sigmas[list_steps[j]]*p + ((long)1);
}
else
{
tmp_exponent = ptr_exponents[list_steps[j]];
powerb = ptr_current_powers[list_steps[j]];
sigma = ptr_current_sigmas[list_steps[j]];
}

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);
tmp_now_sigma_r = tmp_now_sigma_r*ratio;
}
tmp_now_quotient = tmp_now_sigma_r;

tmp_now_robin = tmp_now_quotient/expq(euler);

log2nprime = logq(tmp_now_n);

robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;

if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}
if( 99999 == (numloops%100000) )
{

printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);
printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);
}
}
else
{

for(j=0; j<= numsteps- ((long)2) ; j++)
{

tmp_exponent = ptr_exponents[list_steps[j]];

p = pts_primes[list_steps[j]];

tmp_now_n = tmp_now_n + ((__float128)tmp_exponent)*splogs[list_steps[j]];

powerb = ptr_current_powers[list_steps[j]];

sigma = ptr_current_sigmas[list_steps[j]];

ratio = ((__float128)sigma)/((__float128)powerb);

tmp_now_sigma_r = tmp_now_sigma_r*ratio;

}

tmp_now_n = tmp_now_n + logq((__float128) ptr_primes[current_step- file_offset]);
ratio = ((__float128)1)/( (__float128)ptr_primes[current_step- file_offset] );

tmp_now_sigma_r = tmp_now_sigma_r + (ratio*tmp_now_sigma_r) ;

tmp_now_quotient = tmp_now_sigma_r;
tmp_now_robin = tmp_now_quotient/expq(euler);
log2nprime = logq(tmp_now_n);
robin_bound = expq(euler)*log2nprime;

delta = robin_bound – tmp_now_quotient;

delta_log = logq(delta);

delta_estimate = constant – log2nprime/((__float128) 2);

variation_delta = delta_log – delta_estimate;

if( variation_delta < record_low_variation_delta)
{
record_low_variation_delta = variation_delta;
record_low_log2n = log2nprime;
}

tmp_el_now_robin = tmp_now_robin/logq(tmp_now_n);

tmp_now_robin = tmp_el_now_robin;
if(tmp_now_robin > RecordRobinQuotient)
{
RecordRobinQuotient = tmp_now_robin;
RecordStep = current_step;
}

if( 99999 == (numloops%100000) )
{
printf(“current step number = %ld “, current_step_number+1);

printf(“quotient de Robin: %.30Qf “, tmp_now_robin);

printf(“\nloglog n = %.30Qf\n”, logq(tmp_now_n));

printf(“\nsigma(n’)/n’ = %.30Qf\n”, tmp_now_sigma_r);

printf(“record step is at: %ld\n”, RecordStep+1);

printf(“log(log(n’)) = %.30Qf “, log2nprime);

printf(“Robin upper bound = %.30Qf “, robin_bound);

printf(“sigma(n’)/n’ = %.30Qf \n”, tmp_now_quotient);

}
}

}

if(RecordStep < numprimes)
{
ptr_exponents[RecordStep]++;

p = pts_primes[RecordStep];

ptr_current_powers[RecordStep] = ptr_current_powers[RecordStep]*p;

ptr_current_sigmas[RecordStep] = ptr_current_sigmas[RecordStep]*p + ((long) 1);

}
if(RecordStep == numprimes)
{

if(num_new_primes < 79999500)
{

for(j=0; j< 200 ; j++)
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
}
else
{

sum_logs_primes = sum_logs_primes + logq( (__float128) ptr_primes[numprimes- file_offset]);

ratio = ((__float128)1)/((__float128)ptr_primes[numprimes-file_offset]);

if( RecordStep > 999999 )
{
numBigPrimesUsed++;
}

num_new_primes++;

prod_sigma_r = prod_sigma_r + (prod_sigma_r*ratio) ;

numprimes++;
}
skip_base_case = (int) 1;
}
else
{
skip_base_case = (int) 0;
}

if( 99999 == (numloops%100000) )
{
printf(“=================================\n”);
}
}

}
return 0;
}

Written by meditationatae

January 3, 2015 at 11:33 am

Posted in History

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