M3235657 Mersenne number exponent details

Residue

Status

L-L

9CA495434541C76B

double-checked

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	2⁶⁸	18.4213	67.6471%	1073564	116447100	0.9082	7.5413%	19.3295	70.0869%	2.4398%
PrimeNet	2⁶⁰	0.0475	63.3333%	14000	260000	0.0034	2.7687%	0.0508	64.3485%	1.0152%
GPU72	2⁶⁴	1.1000	65.6250%	16000	280000	0.0037	1.6534%	1.1038	66.1934%	0.5684%
Difference	+4	+17.3212	+2.0221%	+1057564	+116167100	+0.9045	+5.8879%	+18.2257	+3.8935%	+3.8935%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.4213

67.6471%

1073564

116447100

0.9082

7.5413%

19.3295

70.0869%

2.4398%

PrimeNet

2⁶⁰

0.0475

63.3333%

14000

260000

0.0034

2.7687%

0.0508

64.3485%

1.0152%

GPU72

2⁶⁴

1.1000

65.6250%

16000

280000

0.0037

1.6534%

1.1038

66.1934%

0.5684%

Difference

+17.3212

+2.0221%

+1057564

+116167100

+0.9045

+5.8879%

+18.2257

+3.8935%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3235657	4076474156964152143	19	61.822	629929896303 3 × 23 × 7129 × 1280603	2009-05-19	7129	1280603	0.1332	0.0094	0.0161
3235657	733788008250238919421559	24	79.280	113390882941275747 3³ × 4199662331158361	2019-05-07	27	4199662331158361	48,871	28,237,596	52,739,966

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3235657

4076474156964152143

61.822

629929896303
3 × 23 × 7129 × 1280603

2009-05-19

7129

1280603

0.1332

0.0094

0.0161

3235657

733788008250238919421559

79.280

113390882941275747
3³ × 4199662331158361

2019-05-07

4199662331158361

48,871

28,237,596

52,739,966

exponent	prime factors	composite factor	digits	bits*
3235657	4076474156964152143 733788008250238919421559	2991267852322297016509521267151504430250937	43	141.102

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-25T20:19:14	Jocelyn Larouche	Manual testing	107855	107855		-		-	-	0.013	-	-	0.902%
2021-01-16T04:02:55	Jocelyn Larouche	Manual testing	323565	3235657	6	-	skipped known factor: 4076474156964152143	-	-	0.060	-	-	3.384%
2022-01-07T11:58:37	Jocelyn Larouche	Manual testing	1073564	116447100		-	skipped known factor: 4076474156964152143	-	-	0.908	-	-	7.541%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-05T22:54:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2022-04-03T17:18:08	LordJulius	Manual testing	2⁶¹	2⁶³	4076474156964152143	61.822	19	0.038	0.559	0.078
2022-04-03T17:18:08	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.607	-	-
2022-04-03T17:18:08	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.155	-	-
2022-04-03T17:18:08	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.309	-	-
2022-04-03T17:18:08	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.619	-	-
2021-07-23T11:05:10	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.238	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.235 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.235 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
		4076474156964152143	1	0.00000e+0
50000	5000000	733788008250238919421559	2	0.235

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-19T15:57:00	Aca Arsov	backo6400			4076474156964152143	61.822		1		1	-
2019-05-08T01:27:10	J.R. Allen	lapdell	50000	5000000	733788008250238919421559	79.280	2	2		2	0.235

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	9CA495434541C76B	0.275
1999-09-30T00:00:00	ANONYMOUS	v4_computers	9CA495434541C76B	0.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-02T08:48:11

Oliver Kruse

GTX-2

4076474156964152143

A962EBC51E7BC6__

2017-12-13T15:40:41

kkmrkkblmbrbk

c4.xlarge

4076474156964152143

A962EBC51E7BC6__

2019-05-08T15:13:56

Chang Chia-Tche

homura

4076474156964152143

733788008250238919421559

A962EBC51E7BC63B

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1073564, B2 = 116447100 (P-1 stage 2)

B1 = 1073564 (P-1 stage 1)

B1 = 323565, B2 = 3235657 (P-1 stage 2)

B1 = 323565 (P-1 stage 1)

B1 = 107855 (P-1 stage 1)

10⁰

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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