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Euler-Mascheroni Constant good to about 316 decimals… (cf. Knuth 1962)

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57721 56649 01532 86060 65120 90082 40243 10421 59335 93992
35988 05767 23488 48677 26777 66467 09369 47063 29174 67495
14631 44724 98070 82480 96050 40144 86542 83622 41739 97644
92353 62535 00333 74293 73377 37673 94279 25952 58247 09491
60087 35203 94816 56708 53233 15177 66115 28621 19950 15079
84793 74508 57057 40029 92135 47861 46694 02960 43254 21519
05877 55352 67331 39858

Written by meditationatae

September 1, 2014 at 9:19 am

Posted in History

Last puzzle repeated

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15703195571470668455999681160204860299028204353074
42741895752337540667209488970390897552869446548367
95246733248226248184939832865288198575273304314476
42150774293331409286263936871010011874390997386653
92345390984741006335247879104386642699582770369144
80608947188670454346109352574167476486488255327927
82705194635844802883751307757409372112551173305450
91739842110157884671250113142689258777038255738509
42833293355385343492990507851921859192438465746637
91847101663851064671915123475018473756789221059942
75761641984113556229139558377477204934611764071187
72294574048959087741390806736256618390717248111682
18332833597784412775023742557375446667945206368292
92693317446404644661931602094363636242533203136604
06348005774729896935210115229963813500918868121649
90730843939620556981777622075339909235516319038682
79891837295886204693216378244015970882522151224612
49031093249175609616436395473394754792709794175646
46412275555387404128023225225288338759414600615971
74637629106108386252174876254920385403473653588115
91968159531618591609733575737302294830674634211616
78086581027168282022205171905123451733740543429036
49670898542790205267282480265883639313820465807531
13381103780052827441425771788627789560496955181839
08283356238383725820512260770784851644802037403100
69368020811641751663071448691222677052395637433277
25216428958304124212421646093374087069634392349659
68892381266108596521726831160981991556512255079202
72564614024934955726051648290395217254332837154120
35327251887341783438766135317545242885680473740991
06834356830426872975131483989842438484739287241905
58133782585692558047228969894066663361922514691589
24228726181584199070527610341279492358204203731541
29141332972686605783699976283103004974293879297585
15885609721773702116312471626971690794730069616867
74897514965233134287198925481214205193913205444427
50316669232260624511106914286296155932671815419681
89819330708538545607541404383082253457198675255085
86575689383513604003668431080773489124447004535078
75151928532568344339037223157996054643717626877434
93381549869762003683574635750295030762391179620804
46673228973432549391646263401574500944489604804413
93000727367629927548829655673680023483989123924990
49387184027453569898884688266694555744325096760825
[repeated]

 

Written by meditationatae

August 28, 2014 at 9:10 pm

Posted in History

can you find the RSA-2048 modulus?

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I took a 2048-bit RSA modulus from a Certificate that appears when one clicks on the lock icon in the browser at http://www.nsa.gov (GeoTrust Global).  This is originally written as a  256 two-hexit (hexadecimal) array of numbers from 0 to 255 as two hexadecimal values, including the leading zero when required. Then, I converted the 2048-bit modulus to bas ten, which gives a 617-digit number in base 10.

This is very close to 2^2048. Let ‘m’ be the modulus (617 digits). Log means natural logarithm.

I find 2^2048 > m, and I computed log(2^2048) – log(m). This is between 0.0 and 0.2 .

I multiply (log(2^2048) – log(m)) by 10^2200, and take the floor, to get a 2200-digit number k; this 2200-digit number k is displayed in 44 lines, each having 50 digits. What is the modulus m? (in base ten)?

15703195571470668455999681160204860299028204353074
42741895752337540667209488970390897552869446548367
95246733248226248184939832865288198575273304314476
42150774293331409286263936871010011874390997386653
92345390984741006335247879104386642699582770369144
80608947188670454346109352574167476486488255327927
82705194635844802883751307757409372112551173305450
91739842110157884671250113142689258777038255738509
42833293355385343492990507851921859192438465746637
91847101663851064671915123475018473756789221059942
75761641984113556229139558377477204934611764071187
72294574048959087741390806736256618390717248111682
18332833597784412775023742557375446667945206368292
92693317446404644661931602094363636242533203136604
06348005774729896935210115229963813500918868121649
90730843939620556981777622075339909235516319038682
79891837295886204693216378244015970882522151224612
49031093249175609616436395473394754792709794175646
46412275555387404128023225225288338759414600615971
74637629106108386252174876254920385403473653588115
91968159531618591609733575737302294830674634211616
78086581027168282022205171905123451733740543429036
49670898542790205267282480265883639313820465807531
13381103780052827441425771788627789560496955181839
08283356238383725820512260770784851644802037403100
69368020811641751663071448691222677052395637433277
25216428958304124212421646093374087069634392349659
68892381266108596521726831160981991556512255079202
72564614024934955726051648290395217254332837154120
35327251887341783438766135317545242885680473740991
06834356830426872975131483989842438484739287241905
58133782585692558047228969894066663361922514691589
24228726181584199070527610341279492358204203731541
29141332972686605783699976283103004974293879297585
15885609721773702116312471626971690794730069616867
74897514965233134287198925481214205193913205444427
50316669232260624511106914286296155932671815419681
89819330708538545607541404383082253457198675255085
86575689383513604003668431080773489124447004535078
75151928532568344339037223157996054643717626877434
93381549869762003683574635750295030762391179620804
46673228973432549391646263401574500944489604804413
93000727367629927548829655673680023483989123924990
49387184027453569898884688266694555744325096760825

 

Written by meditationatae

August 28, 2014 at 6:14 pm

Posted in History

Leveraging Social Media with Community and Influencers

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meditationatae:

i use twitter to look for experts, names, or expert companies. also, Tweets can register (small)public memos, and provide WordPress Blog post digests by “Tweeting” a Post …

Originally posted on Blog Stu - Stuart Miniman:

The Internet gave us broad access to an endless supply of information (even if it might distract us and prevent us from deeply understanding topics). Mobile technology increasingly allows us to be constantly connected to the Internet, plus communities and connections. Social media, formerly known as Web 2.0, rode on the waves of new Internet and mobile technology, promising to transform business and communication. At EMC World 2014, I hosted a lively segment on theCUBE with two friends – John Troyer and Amy Lewis (2/3 of the Geek Whisperers podcast) – about social media, community and influencers. John recently ended his 9 years of running communities at VMware to launch a new venture, TechReckoning, a new place for the IT community to figure things out together. Amy manages Influencer Marketing for Cisco. When asked if we are now in a “post-social” phase, both John and Amy agreed that…

View original 289 more words

Written by meditationatae

August 18, 2014 at 4:36 am

Posted in History

testing embedded video from ICM2014, Seoul, South Korea…

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<div id=”fb-root”></div> <script>(function(d, s, id) { var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = “//connect.facebook.net/en_GB/all.js#xfbml=1″; fjs.parentNode.insertBefore(js, fjs); }(document, ‘script’, ‘facebook-jssdk’));</script>
<div class=”fb-post” data-href=”https://www.facebook.com/photo.php?v=684176694990013&#8243; data-width=”466″><div class=”fb-xfbml-parse-ignore”><a href=”https://www.facebook.com/photo.php?v=684176694990013″>Post</a&gt; by <a href=”https://www.facebook.com/SEOULICM2014″>The International Congress of Mathematicians 2014</a>.</div></div>

Written by meditationatae

August 16, 2014 at 3:05 pm

Posted in History

Clean vetted C program for Collatz total stopping time records

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I’m copying below a clean copy of my latest C program to find some (but not all) record breaking values of the modified total stopping time to reach ‘1’, based on a small variant of the Lagarias total stopping time function sigma_{oo} (n),  for integers  n at least two, introduced by Jeffrey Lagarias in his 1985 American Mathematical Monthly “cyclopedic” article.

The program now uses two long long int integers to store intermediate (non-printed) computations, due to “blow-up” in the iterates of the T(.) function, following Lagarias1985.

The two long long int values are stored in a one-dimensional array of size 2.  This functions in the code below as “arithmetic modulo 10^15 ” , and is defined  in the first line of code with the token ‘MOD’.

Only integers n such that  n == 27 (mod 100)  are tested. This is a purely empirical criterion, that still appears to catch a healthy proportion of all “record-breaking” n.

David Bernier

Quebec City,

August 16, 2014

12:30 AM

#define MAX 100000000000
#define MOD 1000000000000000
#include <stdio.h>

int main(void)
{
long long n;
long long y[2];
long long steps;
long long maxsteps;
long long modulo2;
long long tmp;
long long ret;

maxsteps = 0;

for(n=27; n< MAX; n=n+100)
{
y[0] = n;
y[1] = 0;
steps = 0;

while(y[0]>1 || y[1]>0)
{
modulo2 = y[0]%2;
if(modulo2 == 0)
{
tmp = y[1]/2;
if(0 == (y[1]%2))
{
y[1] = tmp;
y[0] = y[0]/2;
}
else
{
y[1] = tmp;
y[0] = y[0] + MOD;
y[0] = y[0]/2;
}
}
else
{
y[1] = y[1]+y[1]+y[1];
y[0] = y[0]+y[0]+y[0];
y[0] = y[0]+1;
tmp = y[0]%MOD;
ret = (y[0]-tmp)/MOD;
y[1] = y[1] + ret;
y[0] = tmp;
}

steps++;

}

if(steps > maxsteps)
{
if(maxsteps< 1050)
{
maxsteps = steps;
}

printf(“%lld %lld total steps\n”, n, steps);
}
}

return 0;
}

Written by meditationatae

August 16, 2014 at 4:30 am

Posted in History

Defining a modified Total Stopping Time function for Collatz conjecture

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——————————————–

This below confirms that for n = 12,235,060,455
it takes 1184 iterations of the mapping:

f(k) := 3k+1 (for k>=1 and odd)
f(k) := k/2 (for k>=2 and even)

in order to reach 1.

This of course is related to the Collatz conjecture.
I’ll call this way of counting total steps the
MODIFIED TOTAL STOPPING TIME (in steps), since
in his well-known 1985 article on Collatz,
Jeff Lagarias used the mapping:

T(k) := (3k+1)/2    (for k>=1 and odd)
T(k) := k/2            (for k>=2 and even)

in order to define what he called the
total stopping time (function) for a starting number ‘n’,
in order to reach 1, namely:

sigma_{oo} (n) := min steps of iterating T(k) map so as attain k=1.

n = 27 takes 111 total steps to reach ‘1’ when iterating
the ‘f’ map, but 70 total steps to reach ‘1’ for the Lagarias-kind
‘T’ map.

David Bernier
Quebec City,
August 15, 2014
3:50 pm EDT

———————————————–

 

The computations and steps given here for  ‘n’ as above were produced

using a Web application made in France.  It corroborates the

modified total stopping time of 1184 found by my program on my computer.

It is hoped that this can serve as some sort of fully documented

computation for Collatz experimenters.

Etapes du vol du nombre 12,235,060,455 :

12235060455
36705181366
18352590683
55057772050
27528886025
82586658076
41293329038
20646664519
61939993558
30969996779
92909990338
46454995169
139364985508
69682492754
34841246377
104523739132
52261869566
26130934783
78392804350
39196402175
117589206526
58794603263
176383809790
88191904895
264575714686
132287857343
396863572030
198431786015
595295358046
297647679023
892943037070
446471518535
1339414555606
669707277803
2009121833410
1004560916705
3013682750116
1506841375058
753420687529
2260262062588
1130131031294
565065515647
1695196546942
847598273471
2542794820414
1271397410207
3814192230622
1907096115311
5721288345934
2860644172967
8581932518902
4290966259451
12872898778354
6436449389177
19309348167532
9654674083766
4827337041883
14482011125650
7241005562825
21723016688476
10861508344238
5430754172119
16292262516358
8146131258179
24438393774538
12219196887269
36657590661808
18328795330904
9164397665452
4582198832726
2291099416363
6873298249090
3436649124545
10309947373636
5154973686818
2577486843409
7732460530228
3866230265114
1933115132557
5799345397672
2899672698836
1449836349418
724918174709
2174754524128
1087377262064
543688631032
271844315516
135922157758
67961078879
203883236638
101941618319
305824854958
152912427479
458737282438
229368641219
688105923658
344052961829
1032158885488
516079442744
258039721372
129019860686
64509930343
193529791030
96764895515
290294686546
145147343273
435442029820
217721014910
108860507455
326581522366
163290761183
489872283550
244936141775
734808425326
367404212663
1102212637990
551106318995
1653318956986
826659478493
2479978435480
1239989217740
619994608870
309997304435
929991913306
464995956653
1394987869960
697493934980
348746967490
174373483745
523120451236
261560225618
130780112809
392340338428
196170169214
98085084607
294255253822
147127626911
441382880734
220691440367
662074321102
331037160551
993111481654
496555740827
1489667222482
744833611241
2234500833724
1117250416862
558625208431
1675875625294
837937812647
2513813437942
1256906718971
3770720156914
1885360078457
5656080235372
2828040117686
1414020058843
4242060176530
2121030088265
6363090264796
3181545132398
1590772566199
4772317698598
2386158849299
7158476547898
3579238273949
10737714821848
5368857410924
2684428705462
1342214352731
4026643058194
2013321529097
6039964587292
3019982293646
1509991146823
4529973440470
2264986720235
6794960160706
3397480080353
10192440241060
5096220120530
2548110060265
7644330180796
3822165090398
1911082545199
5733247635598
2866623817799
8599871453398
4299935726699
12899807180098
6449903590049
19349710770148
9674855385074
4837427692537
14512283077612
7256141538806
3628070769403
10884212308210
5442106154105
16326318462316
8163159231158
4081579615579
12244738846738
6122369423369
18367108270108
9183554135054
4591777067527
13775331202582
6887665601291
20662996803874
10331498401937
30994495205812
15497247602906
7748623801453
23245871404360
11622935702180
5811467851090
2905733925545
8717201776636
4358600888318
2179300444159
6537901332478
3268950666239
9806851998718
4903425999359
14710277998078
7355138999039
22065416997118
11032708498559
33098125495678
16549062747839
49647188243518
24823594121759
74470782365278
37235391182639
111706173547918
55853086773959
167559260321878
83779630160939
251338890482818
125669445241409
377008335724228
188504167862114
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282756251793172
141378125896586
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212067188844880
106033594422440
53016797211220
26508398605610
13254199302805
39762597908416
19881298954208
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1863871776958
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1397903832719
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2096855749079
6290567247238
3145283623619
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14153776306288
7076888153144
3538444076572
1769222038286
884611019143
2653833057430
1326916528715
3980749586146
1990374793073
5971124379220
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1492781094805
4478343284416
2239171642208
1119585821104
559792910552
279896455276
139948227638
69974113819
209922341458
104961170729
314883512188
157441756094
78720878047
236162634142
118081317071
354243951214
177121975607
531365926822
265682963411
797048890234
398524445117
1195573335352
597786667676
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149446666919
448340000758
224170000379
672510001138
336255000569
1008765001708
504382500854
252191250427
756573751282
378286875641
1134860626924
567430313462
283715156731
851145470194
425572735097
1276718205292
638359102646
319179551323
957538653970
478769326985
1436307980956
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359076995239
1077230985718
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1022527849727
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6551567599673
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11055770324450
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12437741615008
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3109435403752
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368941798397
1106825395192
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207529761599
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311294642399
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1400825890798
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4727787381448
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1181946845362
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1772920268044
886460134022
443230067011
1329690201034
664845100517
1994535301552
997267650776
498633825388
249316912694
124658456347
373975369042
186987684521
560963053564
280481526782
140240763391
420722290174
210361145087
631083435262
315541717631
946625152894
473312576447
1419937729342
709968864671
2129906594014
1064953297007
3194859891022
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4792289836534
2396144918267
7188434754802
3594217377401
10782652132204
5391326066102
2695663033051
8086989099154
4043494549577
12130483648732
6065241824366
3032620912183
9097862736550
4548931368275
13646794104826
6823397052413
20470191157240
10235095578620
5117547789310
2558773894655
7676321683966
3838160841983
11514482525950
5757241262975
17271723788926
8635861894463
25907585683390
12953792841695
38861378525086
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27665961860146
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10374735697555
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23343155319500
11671577659750
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13130524867220
6565262433610
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4923946825208
2461973412604
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1

 

 

Written by meditationatae

August 15, 2014 at 7:59 pm

Posted in History

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