M3255437 Mersenne number exponent details

Residue

Status

L-L

7B41A2EFBA6FD1E3

double-checked

PRP

F5067A795B39F998

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	36.6730	68.1159%	4000000	150000000	1.8206	8.1120%	38.4936	70.7024%	2.5864%
PrimeNet	2⁶⁰	0.0472	63.3333%	14000	260000	0.0042	2.7717%	0.0514	64.3496%	1.0163%
GPU72	2⁶⁴	1.0933	65.6250%	16000	280000	0.0046	1.6554%	1.0980	66.1940%	0.5690%
Difference	+5	+35.5797	+2.4909%	+3984000	+149720000	+1.8159	+6.4566%	+37.3956	+4.5083%	+4.5083%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

36.6730

68.1159%

4000000

150000000

1.8206

8.1120%

38.4936

70.7024%

2.5864%

PrimeNet

2⁶⁰

0.0472

63.3333%

14000

260000

0.0042

2.7717%

0.0514

64.3496%

1.0163%

GPU72

2⁶⁴

1.0933

65.6250%

16000

280000

0.0046

1.6554%

1.0980

66.1940%

0.5690%

Difference

+35.5797

+2.4909%

+3984000

+149720000

+1.8159

+6.4566%

+37.3956

+4.5083%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3255437	20615499612758878091095487	26	84.092	3166318318056666139 17467 × 181274306867617	2021-04-03	17467	181274306867617	2,021,177	1,504,068	2,809,180

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3255437

20615499612758878091095487

84.092

3166318318056666139
17467 × 181274306867617

2021-04-03

17467

181274306867617

2,021,177

1,504,068

2,809,180

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T05:40:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.670%
2011-09-12T23:46:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.696%
2014-06-11T02:10:00	Jocelyn Larouche	Manual testing	79716	79716		-		-	-	0.012	-	-	0.651%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	99432	99432		-		-	-	0.015	-	-	0.746%
2016-01-17T13:12:29	Jocelyn Larouche	Manual testing	415800	4158000	6	-		-	-	0.094	-	-	3.334%
2020-08-12T01:26:37	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.112%
2022-03-24T08:47:00	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.011%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-04T07:03:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-18T20:19:00	markr	Manual testing	2¹	2⁶²		-	-	0.189	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.302	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.603	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.148	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.295	-	-
2017-03-30T02:15:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.591	-	-
2019-01-07T14:44:15	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.182	-	-
2021-02-07T12:22:03	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.36	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.795 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	5.795 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.213	29.745%
25	50000	0.113	89.340%
30	250000	0.007	99.278%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	3.199
50000	5000000	20615499612758878091095487	5	0.727
50000	6450000		3	0.493
80000	11280000		5	1.376

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-30T05:28:00	Stun	Core2	50000	5000000						3	0.436
2011-09-23T21:45:00	Huaiyu Wu	eight	50000	5000000						3	0.436
2014-06-10T22:22:00	ecjahns	Ethan_J_1	50000	5000000						3	0.436
2016-08-31T09:12:06	Richard Kint	Desktop	50000	5000000						3	0.436
2018-12-20T16:09:47	Volki		50000	5000000						3	0.436
2020-12-31T05:16:36	axn	Manual testing	50000	6450000						3	0.493
2021-01-24T06:41:44	Zenzoma	AMD3970X	50000	5000000						7	1.018
2021-01-25T09:23:41	axn	Manual testing	80000	11280000						5	1.376
2021-04-03T00:09:56	mnd9	50869	50000	5000000	20615499612758878091095487	84.092	5	2	918546068399949	5	0.727

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	7B41A2EFBA6FD1E3	0.342
1999-06-26T00:00:00	ANONYMOUS	v4_computers	7B41A2EFBA6FD1E3	0.342

date

userid

compid

res64

spent (GHz-days)

1998-02-08T00:00:00

ANONYMOUS

v4_computers

7B41A2EFBA6FD1E3

0.342

1999-06-26T00:00:00

ANONYMOUS

v4_computers

7B41A2EFBA6FD1E3

0.342

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 415800, B2 = 4158000 (P-1 stage 2)

B1 = 415800 (P-1 stage 1)

B1 = 60000, B2 = 1050000 (P-1 stage 2)

B1 = 99432 (P-1 stage 1)

B1 = 79716 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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