M3256987 Mersenne number exponent details

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M3256987

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is 2 ^3256987 - 1

has 980451 decimal digits

takes 0.342 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	AD3B3963212B79B6	double-checked
PRP	37B956BC0DF55554	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	2⁶⁸	18.3006	67.6471%	4000000	150000000	1.8206	8.7755%	20.1212	70.4862%	2.8391%
PrimeNet	2⁶⁰	0.0472	63.3333%	14000	260000	0.0042	2.7719%	0.0513	64.3497%	1.0164%
GPU72	2⁶⁴	1.0928	65.6250%	16000	280000	0.0046	1.6555%	1.0975	66.1941%	0.5691%
Difference	+4	+17.2078	+2.0221%	+3984000	+149720000	+1.8159	+7.1200%	+19.0237	+4.2921%	+4.2921%

Known prime factors (1 factor, 92.4 bits, 0.00283834% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3256987	6738653948911273681153726873	28	92.445	1034491993506770779428 2² × 3 × 7² × 17 × 509 × 911 × 3677 × 60697541	2020-08-26	3677	60697541	543,103,700	0.5041	0.9406

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-05T09:06:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.785%
2011-09-13T15:37:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.929%
2014-06-11T02:11:00	Jocelyn Larouche	Manual testing	79707	79707		-		-	-	0.012	-	-	0.754%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	99414	99414		-		-	-	0.015	-	-	0.861%
2016-01-18T12:25:10	Jocelyn Larouche	Manual testing	415800	4158000	6	-		-	-	0.094	-	-	3.697%
2020-08-26T04:58:07	mikr	MSI	4000000	150000000	12		6738653948911273681153726873	28	92.445	1.821	0.684	3.641	8.776%
2021-01-18T13:43:04	Jocelyn Larouche	Manual testing	445800	3256987	6	-		-	-	0.091	-	-	3.513%
2022-01-06T11:34:48	Jocelyn Larouche	Manual testing	1297196	116447100		-	skipped known factor: 6738653948911273681153726873	-	-	1.153	-	-	7.696%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:33:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-16T21:21:00	markr	Manual testing	2¹	2⁶²		-	-	0.189	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.301	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.603	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.147	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.294	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.294	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.589	-	-
2017-03-30T02:15:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.589	-	-
2019-01-07T14:44:14	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.177	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.181 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	2.181 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.181

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-19T22:16:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.436
2011-09-19T23:44:00	sannerud.com	Jim2010	50000	5000000						3	0.436
2014-06-13T01:33:00	joe b.	Pandora	50000	5000000						3	0.436
2016-08-29T08:57:30	Dennis Schreiber	z400	50000	5000000						3	0.436
2018-12-21T13:57:29	volki	home	50000	5000000						3	0.436

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	AD3B3963212B79B6	0.342
2009-04-02T18:46:00	ANONYMOUS	computer	AD3B3963212B79B6	0.342

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-26T21:08:22

jvang

3600

6738653948911273681153726873

37B956BC0DF55554

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 = 1297196, B2 = 116447100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1297196 (P-1 stage 1)

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

B1 = 445800, B2 = 3256987 (P-1 stage 2)

B1 = 445800 (P-1 stage 1)

B1 = 415800 (P-1 stage 1)

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

B1 = 99414 (P-1 stage 1)

B1 = 79707 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-06T11:34:48+00:00

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