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memo on program output, december 23, 4:31 am

the program
/home/david2/eratosthenes4/superabun3642a.out is working fine.
compilation command with gcc (GCC) 4.9.2 :
$ /usr/local/bin/gcc -lquadmath -O2 -o superabun3642a.out superabun3642a.c

GCC’s libquadmath 128-bit floats math library is used.

Command line for execution:

$ ./superabun3642a.out > output3642 &

Many of most numbers produced are
colossally abundant numbers, as
verified by exponent calculations using
the Erdos-Alaoglu critical exponents
formula:

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

for a prime Y and critical exponent epsilon.
/**********************************

$ date
Tue Dec 23 04:26:25 EST 2014

$ pwd
/home/david2/eratosthenes4
*********************************/
=================================
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 11
step at 15
step at 22
step at 35
step at 78
step at 260
step at 2033
step at 144567
step at 70459987801

Number of big primes used in making current n is: 70458987800
numloops = 299999
————————
? for(X=1,1,print(X,” “,g(prime(X))));for(X=2,200000, if(g(prime(X-1))>g(prime(X)),print(X,” “,g(prime(X)))))

1 45
2 28
3 19
4 15
5 12
6 11
7 10
9 9
11 8
15 7
22 6
35 5
78 4
260 3
2033 2
144567 1
———————–
number of steps: 17
45 28 19 15 12 11 10 10 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 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 4 4 4 4 4 4 4 4
current step number = 1 quotient de Robin: 0.999999979969639950916521117309
loglog n = 28.283119174487206807008183418521

sigma(n’)/n’ = 50.374282447393826939659200072507
record step is at: 1
log(log(n’)) = 28.283119174487206807008183418521 Robin upper bound = 50.374283456408861786118087102018 sigma(n’)/n’ = 50.374282447393826939659200072507
current step number = 2 quotient de Robin: 0.999999979969635091029114148087
loglog n = 28.283119174487418034722160453257

sigma(n’)/n’ = 50.374282447393958338161139131519
record step is at: 1
log(log(n’)) = 28.283119174487418034722160453257 Robin upper bound = 50.374283456409237997973366721214 sigma(n’)/n’ = 50.374282447393958338161139131519
current step number = 3 quotient de Robin: 0.999999979969624356780703349851
loglog n = 28.283119174487684150169806254315

sigma(n’)/n’ = 50.374282447393891578963311306779
record step is at: 1
log(log(n’)) = 28.283119174487684150169806254315 Robin upper bound = 50.374283456409711968857169772045 sigma(n’)/n’ = 50.374282447393891578963311306779
current step number = 4 quotient de Robin: 0.999999979969635562605689457235
loglog n = 28.283119174487859435934072920616

sigma(n’)/n’ = 50.374282447394768261001272677234
record step is at: 1
log(log(n’)) = 28.283119174487859435934072920616 Robin upper bound = 50.374283456410024165497171463236 sigma(n’)/n’ = 50.374282447394768261001272677234
current step number = 5 quotient de Robin: 0.999999979969627778566175212813
loglog n = 28.283119174488094898326596079569

sigma(n’)/n’ = 50.374282447394795521152742963566
record step is at: 1
log(log(n’)) = 28.283119174488094898326596079569 Robin upper bound = 50.374283456410443541069968443068 sigma(n’)/n’ = 50.374282447394795521152742963566
current step number = 6 quotient de Robin: 0.999999979969637988734051302197
loglog n = 28.283119174488181925426359456088

sigma(n’)/n’ = 50.374282447395464852607372120054
record step is at: 1
log(log(n’)) = 28.283119174488181925426359456088 Robin upper bound = 50.374283456410598542636974674271 sigma(n’)/n’ = 50.374282447395464852607372120054
current step number = 7 quotient de Robin: 0.999999979969620889290634426619
loglog n = 28.283119174488321677990754196879

sigma(n’)/n’ = 50.374282447394852389830544696947
record step is at: 1
log(log(n’)) = 28.283119174488321677990754196879 Robin upper bound = 50.374283456410847452074761546102 sigma(n’)/n’ = 50.374282447394852389830544696947
current step number = 8 quotient de Robin: 0.999999979969610949083138726347
loglog n = 28.283119174488479151707401603662

sigma(n’)/n’ = 50.374282447394632131088201886610
record step is at: 1
log(log(n’)) = 28.283119174488479151707401603662 Robin upper bound = 50.374283456411127924168040646195 sigma(n’)/n’ = 50.374282447394632131088201886610
current step number = 9 quotient de Robin: 0.999999979969618963443054422556
loglog n = 28.283119174488634652120014070114

sigma(n’)/n’ = 50.374282447395312806216659461535
record step is at: 1
log(log(n’)) = 28.283119174488634652120014070114 Robin upper bound = 50.374283456411404881663930805299 sigma(n’)/n’ = 50.374282447395312806216659461535
current step number = 10 quotient de Robin: 0.999999979969615799494961387814
loglog n = 28.283119174488851451562421373895

sigma(n’)/n’ = 50.374282447395539560097952417780
record step is at: 1
log(log(n’)) = 28.283119174488851451562421373895 Robin upper bound = 50.374283456411791017171038108513 sigma(n’)/n’ = 50.374282447395539560097952417780
current step number = 11 quotient de Robin: 0.999999979969616544657695908455
loglog n = 28.283119174489121981880915878674

sigma(n’)/n’ = 50.374282447396058931215611659906
record step is at: 1
log(log(n’)) = 28.283119174489121981880915878674 Robin upper bound = 50.374283456412272851259538774518 sigma(n’)/n’ = 50.374282447396058931215611659906
current step number = 12 quotient de Robin: 0.999999979969644217377550463723
loglog n = 28.283119174489452524892311563683

sigma(n’)/n’ = 50.374282447398041645678338897166
record step is at: 35
log(log(n’)) = 28.283119174489452524892311563683 Robin upper bound = 50.374283456412861572300095048784 sigma(n’)/n’ = 50.374282447398041645678338897166
current step number = 13 quotient de Robin: 0.999999979969636540333246559778
loglog n = 28.283119174489963052279120371866

sigma(n’)/n’ = 50.374282447398564206301527047151
record step is at: 35
log(log(n’)) = 28.283119174489963052279120371866 Robin upper bound = 50.374283456413770858547368829881 sigma(n’)/n’ = 50.374282447398564206301527047151
current step number = 14 quotient de Robin: 0.999999979969641646483053037004
loglog n = 28.283119174490707402435181182845

sigma(n’)/n’ = 50.374282447400147166444980975124
record step is at: 35
log(log(n’)) = 28.283119174490707402435181182845 Robin upper bound = 50.374283456415096600079655439715 sigma(n’)/n’ = 50.374282447400147166444980975124
current step number = 15 quotient de Robin: 0.999999979969645552700778606433
loglog n = 28.283119174491941511507170828415

sigma(n’)/n’ = 50.374282447402541976948816047184
record step is at: 2033
log(log(n’)) = 28.283119174491941511507170828415 Robin upper bound = 50.374283456417294637708567677065 sigma(n’)/n’ = 50.374282447402541976948816047184
current step number = 16 quotient de Robin: 0.999999979969645611243283607492
loglog n = 28.283119174494387232690687814358

sigma(n’)/n’ = 50.374282447406900932440361311378
record step is at: 144567
log(log(n’)) = 28.283119174494387232690687814358 Robin upper bound = 50.374283456421650644250624123969 sigma(n’)/n’ = 50.374282447406900932440361311378

current step number = 17
quotient de Robin: 0.999999979969645612769119569220
log(log(n’)) = 28.283119174501579848150233627367
Robin upper bound = 50.374283456434461213258831064204
sigma(n’)/n’ = 50.374282447419711578054861258561

record step is at: 70459987801
=================================

? log(50.374283456434461213258831064204-50.374282447419711578054861258561)
-((323336/1000000)-28.283119174501579848150233627367/2)

%3398 =

0.01168738862369575379063454311627168294500697501701265944607302210699198
? prime(70459987801)
time = 2h, 1min, 30,758 ms.
%3389 = 1,919,563,670,117

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Written by meditationatae

December 23, 2014 at 9:31 am

Posted in History

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