M2096377 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	14.1739	68.6567%	500000	15000000	0.1230	5.1521%	14.2969	70.2716%	1.6148%
PrimeNet	2⁵⁸	0.0183	63.7931%	9000	160000	0.0016	2.6769%	0.0200	64.7623%	0.9692%
GPU72	2⁶²	0.2931	66.1290%	9000	140000	0.0015	1.4012%	0.2946	66.6036%	0.4746%
Difference	+5	+13.8809	+2.5277%	+491000	+14860000	+0.1214	+3.7510%	+14.0023	+3.6679%	+3.6679%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.1739

68.6567%

500000

15000000

0.1230

5.1521%

14.2969

70.2716%

1.6148%

PrimeNet

2⁵⁸

0.0183

63.7931%

9000

160000

0.0016

2.6769%

0.0200

64.7623%

0.9692%

GPU72

2⁶²

0.2931

66.1290%

9000

140000

0.0015

1.4012%

0.2946

66.6036%

0.4746%

Difference

+13.8809

+2.5277%

+491000

+14860000

+0.1214

+3.7510%

+14.0023

+3.6679%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2096377	251565241	9	27.906	60 2² × 3 × 5	-	4	5	8.640e-12	3.865e-7	7.761e-7
2096377	375922323641	12	38.452	89660 2² × 5 × 4483	2008-07-15	5	4483	2.458e-8	2.374e-5	4.348e-5
2096377	25634347016857	14	44.543	6113964 2² × 3 × 467 × 1091	2008-08-26	467	1091	1.530e-6	4.776e-5	9.061e-5
2096377	307803705976009	15	48.129	73413252 2² × 3² × 11 × 89 × 2083	2008-08-26	89	2083	2.351e-5	1.884e-5	2.019e-5
2096377	4588792195471197700414991	25	81.924	1094457770589735935 5 × 218891554117947187	2022-06-03	5	218891554117947187	393,141	1.137e+9	2.124e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2096377

251565241

27.906

60
2² × 3 × 5

8.640e-12

3.865e-7

7.761e-7

2096377

375922323641

38.452

89660
2² × 5 × 4483

2008-07-15

4483

2.458e-8

2.374e-5

4.348e-5

2096377

25634347016857

44.543

6113964
2² × 3 × 467 × 1091

2008-08-26

467

1091

1.530e-6

4.776e-5

9.061e-5

2096377

307803705976009

48.129

73413252
2² × 3² × 11 × 89 × 2083

2008-08-26

2083

2.351e-5

1.884e-5

2.019e-5

2096377

4588792195471197700414991

81.924

1094457770589735935
5 × 218891554117947187

2022-06-03

218891554117947187

393,141

1.137e+9

2.124e+9

exponent	prime factors	composite factor	digits	bits*
2096377	251565241 375922323641	94568989944028162481	20	66.358
2096377	251565241 25634347016857	6448710685173262267537	22	72.450
2096377	251565241 307803705976009	77432713474547844303169	23	76.035
2096377	375922323641 25634347016857	9636523295596620036616337	25	82.995
2096377	375922323641 307803705976009	115710284375812461079528769	27	86.581
2096377	25634347016857 307803705976009	7890347012063635452760583713	28	92.672
2096377	251565241 4588792195471197700414991	1154380614552630958063543010927831	34	109.831
2096377	251565241 375922323641 25634347016857	2424214305258877958296817641942217	34	110.901
2096377	251565241 375922323641 307803705976009	29108685575179796342274774939918329	35	114.487
2096377	375922323641 4588792195471197700414991	1725029424827218516429299206710102231	37	120.376
2096377	251565241 25634347016857 307803705976009	1984937047663418360009860357061519833	37	120.579
2096377	25634347016857 4588792195471197700414991	117630691526953780397097902931772503287	39	126.468
2096377	307803705976009 4588792195471197700414991	1412447243719821354884862463725989950919	40	130.053
2096377	375922323641 25634347016857 307803705976009	2966157583108783297959705717446459459033	40	131.124
2096377	251565241 375922323641 4588792195471197700414991	433957442988750609445199114397135684876152671	45	148.282
2096377	251565241 25634347016857 4588792195471197700414991	29591793262974785761457009651625956346567447167	47	154.374
2096377	251565241 307803705976009 4588792195471197700414991	355322631266162595618556952939082419966516406479	48	157.960
2096377	251565241 375922323641 25634347016857 307803705976009	746182147238738599568008177098496478408366271953	48	159.030
2096377	375922323641 25634347016857 4588792195471197700414991	44220002890310155509286279363080185722440350307967	50	164.919
2096377	375922323641 307803705976009 4588792195471197700414991	53097044987948108809773038338057421707248602337607 9	51	168.505
2096377	25634347016857 307803705976009 4588792195471197700414991	36207162788517094576513738021721065871399627495641 583	53	174.597
2096377	251565241 375922323641 25634347016857 4588792195471197700414991	11124215684121570835441080605966593423590465833348 142575047	59	192.826
2096377	251565241 375922323641 307803705976009 4588792195471197700414991	13357370918781008088224777544815654763622626093973 4947270039	60	196.411
2096377	251565241 25634347016857 307803705976009 4588792195471197700414991	91084636328195349297604714452451231707155222982513 01277016503	61	202.503
2096377	375922323641 25634347016857 307803705976009 4588792195471197700414991	13611080767907295265853203262084113612335770453063 417481463563703	65	213.048
2096377	251565241 375922323641 25634347016857 307803705976009 4588792195471197700414991	34240748136490637992125201492481762031586286669455 77807007994435664047423	73	240.955

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T13:44:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 251565241 skipped known factor: 375922323641 skipped known factor: 25634347016857 skipped known factor: 307803705976009	-	-	0.123	-	-	5.152%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T13:44:25

alpertron

Manual testing

500000

15000000

skipped known factor: 251565241
skipped known factor: 375922323641
skipped known factor: 25634347016857
skipped known factor: 307803705976009

0.123

-

-

5.152%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	25634347016857	44.543	14	4.12327e-7	0.298	8.91824e-7
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	307803705976009	48.129	15	5.62158e-6	0.298	1.21576e-5
2008-07-15T07:50:00	J Feitsma	Manual testing	?	?	375922323641	38.452	12	7.10804e-9	0.298	1.53741e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

25634347016857

44.543

4.12327e-7

0.298

8.91824e-7

2008-08-26T20:20:00

ANONYMOUS

Manual testing

307803705976009

48.129

5.62158e-6

0.298

1.21576e-5

2008-07-15T07:50:00

J Feitsma

Manual testing

375922323641

38.452

7.10804e-9

0.298

1.53741e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.760 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	2.760 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	1.208	29.869%
25	50000	0.112	89.425%
30	250000	0.007	99.294%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	1.106
50000	6500000	4588792195471197700414991	3	0.286
50000	6625645		7	0.674
50000	7000000		7	0.693

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-04T20:24:59	ATH	ec2-1xd	50000	5000000						3	0.255
2019-08-26T01:54:50	J.R. Allen	lapdell	50000	5000000						3	0.255
2021-10-02T17:37:09	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.596
2022-02-15T01:44:37	Team_Inspector	SpudBoy4	50000	7000000						7	0.693
2022-06-03T06:22:45	debrouxl	o9020	50000	6500000	4588792195471197700414991	81.924	3	2	5284231406924173	3	0.286
2022-06-30T13:11:39	debrouxl	o9020	50000	6625645						7	0.674