M3137471 Mersenne number exponent details

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M3137471

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>>>

is 2 ^3137471 - 1

has 944473 decimal digits

takes 0.267 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

1 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	61EEBBA7A467BD__	unverified 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	18.9977	67.6471%	3137471	637437570	4.6521	10.4150%	23.6498	71.0166%	3.3695%
PrimeNet	2⁶⁰	0.0490	63.3333%	13000	240000	0.0031	2.6479%	0.0521	64.3042%	0.9709%
GPU72	2⁶⁴	1.1345	65.6250%	15000	240000	0.0034	1.5430%	1.1378	66.1554%	0.5304%
Difference	+4	+17.8633	+2.0221%	+3122471	+637197570	+4.6487	+8.8719%	+22.5120	+4.8612%	+4.8612%

Known prime factors (1 factor, 79.6 bits, 0.00253694% 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
3137471	913433867664558932061919	24	79.596	145568495719093329 3³ × 43 × 167 × 4639 × 161843153	2020-11-16	4639	161843153	45,180	1.0887	2.0324

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.251%
2009-07-03T00:56:00	Carsten Kossendey	leela	15000	183750		-		-	-	0.003	-	-	0.769%
2011-09-05T04:56:00	Squeeky_Squirrel	T7500_2200	55000	935000		-		-	-	0.013	-	-	1.823%
2013-09-01T00:15:00	Squeeky_Squirrel	T7500_2200	110000	2475000		-		-	-	0.029	-	-	2.683%
2016-11-07T02:21:08	Squeeky_Squirrel	P4_2600	195000	5460000	12	-		-	-	0.059	-	-	3.527%
2017-01-10T17:24:07	Jocelyn Larouche	low 4M	132000	132000		-		-	-	0.016	-	-	1.005%
2018-07-15T19:00:15	Jocelyn Larouche	low 4M	674000	2696000		-		-	-	0.097	-	-	3.450%
2018-07-16T10:16:46	Jocelyn Larouche	low 4M	674000	4044000		-		-	-	0.106	-	-	3.829%
2019-02-02T19:34:29	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.057%
2021-01-17T00:34:24	Jocelyn Larouche	Manual testing	704000	3137471	6	-		-	-	0.103	-	-	3.603%
2021-11-22T00:58:59	Jocelyn Larouche	Manual testing	3137471	3137471		-		-	-	0.387	-	-	3.771%
2021-12-19T09:29:31	Jocelyn Larouche	Manual testing	3137471	108997350		-		-	-	1.099	-	-	8.192%
2021-12-22T09:19:36	Jocelyn Larouche	Manual testing	3137471	637437570		-	skipped known factor: 913433867664558932061919	-	-	4.652	-	-	10.415%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-10T19:14:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-09T06:39:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-07T14:05:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.313	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.626	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.191	-	-
2015-06-14T13:51:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.382	-	-
2021-02-18T11:47:35	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.382	-	-
2021-02-18T21:10:23	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.764	-	-
2017-04-17T17:51:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.764	-	-
2019-01-07T14:44:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.53	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.575 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	2.575 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.710	49.180%
25	50000	0.064	93.787%
30	250000	0.004	99.606%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.756
50000	5000000	913433867664558932061919	7	0.819

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-30T10:45:00	Anu Järvi	Anu	50000	5000000						3	0.351
2011-07-31T14:31:00	Smurgs	Praca	50000	5000000						3	0.351
2014-02-02T06:58:00	Richard Kint	Desktop	50000	5000000						3	0.351
2016-06-07T22:54:24	prime_dive	erazer	50000	5000000						3	0.351
2018-01-24T03:08:39	alpertron	laptop2	50000	5000000						3	0.351
2020-11-16T18:53:17	daveward2005	Dave2	50000	5000000	913433867664558932061919	79.596	7	2	6890610214465877	7	0.819

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	F4AE02E5C35CE9__	0.267

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-11-19T21:48:11

arnaud

SRV-130

913433867664558932061919

61EEBBA7A467BD__

2020-12-17T12:55:12

Oliver Kruse

IOS-5

913433867664558932061919

61EEBBA7A467BD57

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 = 3137471, B2 = 637437570 (P-1 stage 2)

B1 = 3137471, B2 = 108997350 (P-1 stage 2)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3137471 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 674000, B2 = 4044000 (P-1 stage 2)

B1 = 704000, B2 = 3137471 (P-1 stage 2)

B1 = 674000, B2 = 2696000 (P-1 stage 2)

B1 = 704000 (P-1 stage 1)

B1 = 674000 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 110000, B2 = 2475000 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 55000, B2 = 935000 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 183750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (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: 2021-12-22T09:19:36+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