M3107831 Mersenne number exponent details

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M3107831

<<<

>>>

is 2 ^3107831 - 1

has 935551 decimal digits

takes 0.265 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	-unknown-	-unknown-
PRP	E11C1FEE53C3BD81	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	38.4148	68.1159%	3000000	100000000	1.0224	7.4200%	39.4373	70.4817%	2.3658%
PrimeNet	2⁶⁰	0.0494	63.3333%	13000	240000	0.0031	2.6434%	0.0526	64.3026%	0.9692%
GPU72	2⁶⁴	1.1453	65.6250%	14000	240000	0.0032	1.5079%	1.1485	66.1433%	0.5183%
Difference	+5	+37.2696	+2.4909%	+2986000	+99760000	+1.0192	+5.9122%	+38.2887	+4.3384%	+4.3384%

Known prime factors (1 factor, 75.0 bits, 0.00241366% 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
3107831	38103302307066921530351	23	75.012	6130208223527425 5² × 59 × 67 × 541 × 114659789	2021-07-25	541	114659789	3,466.7	0.7710	1.4399

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	-	-	0.202%
2009-07-03T21:37:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.651%
2011-08-22T22:42:00	Squeeky_Squirrel	T7500_2200	100000	2125000		-		-	-	0.026	-	-	2.253%
2016-08-31T03:20:25	Jocelyn Larouche	low4M	100000	4250000	6	-		-	-	0.040	-	-	2.635%
2016-12-28T01:45:57	Jocelyn Larouche	low 4M	120000	120000		-		-	-	0.015	-	-	0.827%
2017-01-19T17:19:12	Jocelyn Larouche	low 4M	156000	156000		-		-	-	0.019	-	-	0.960%
2017-02-04T18:42:41	Jocelyn Larouche	low 4M	187200	187200		-		-	-	0.023	-	-	1.060%
2017-02-16T04:19:50	Jocelyn Larouche	low 4M	224640	2246400	6	-		-	-	0.041	-	-	2.631%
2017-03-11T20:20:07	Jocelyn Larouche	low 4M	269568	2695680	6	-		-	-	0.050	-	-	2.825%
2018-08-17T15:08:23	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.420%
2022-02-20T22:18:57	Jocelyn Larouche	Manual testing	1000000	128282700		-	skipped known factor: 38103302307066921530351	-	-	0.979	-	-	6.929%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-02-12T16:02:00	Sturle Sunde	gollumilla.ifi	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-22T20:11:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.632	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.202	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.404	-	-
2017-04-11T13:39:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.809	-	-
2019-02-04T14:28:19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.62	-	-
2021-03-03T10:19:23	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.24	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.995 GHz-days
Estimated T-Level:	3.350

Digits	B1	Curves	Complete	FacMiss
20	11000	67 / 100	0.670	50.999%
25	50000	67 / 280	0.239	78.685%

New Calculation Method

Total ECM effort:	7.995 GHz-days
Estimated T-Level:	3.350

Digits	B1	Complete	FacMiss
20	11000	2.609	7.361%
25	50000	0.241	78.581%
30	250000	0.015	98.489%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4800000		7	0.803
50000	5000000		50	5.843
50000	6750000		7	0.945
50000	6750000	38103302307066921530351	3	0.405

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-23T00:28:00	borkencode	CFF2DC1CD	50000	5000000						3	0.351
2011-07-17T08:04:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.351
2013-12-04T11:10:00	Bruce	fx6840-21	50000	5000000						3	0.351
2016-05-15T20:31:45	yooper		50000	5000000						3	0.351
2017-11-26T17:10:53	Volki		50000	5000000						3	0.351
2020-11-06T01:46:54	mnd9	libproj	50000	5000000						7	0.818
2020-12-09T19:33:20	Denis Porva	Yrok	50000	5000000						7	0.818
2021-01-11T11:49:30	mnd9	l2lounge	50000	5000000						7	0.818
2021-02-10T23:52:40	RIHATEC	i7-3770K	50000	5000000						7	0.818
2021-05-14T07:35:08	Anton Evers	windows_laptop	50000	5000000						7	0.818
2021-05-16T00:32:55	kutens	rigel	50000	4800000						7	0.803
2021-06-09T02:24:52	Stef42	AMD-DESKTOP	50000	6750000						7	0.945
2021-07-25T04:38:28	kutens	terra	50000	6750000	38103302307066921530351	75.012	3	2	5069109324735172	3	0.405

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	F317817898D5DC__	0.265

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-26T20:29:18

kutens

canopus

38103302307066921530351

E11C1FEE53C3BD81

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

B1 = 1000000, B2 = 128282700 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 269568, B2 = 2695680 (P-1 stage 2)

B1 = 224640, B2 = 2246400 (P-1 stage 2)

B1 = 100000, B2 = 4250000 (P-1 stage 2)

B1 = 269568 (P-1 stage 1)

B1 = 224640 (P-1 stage 1)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 187200 (P-1 stage 1)

B1 = 156000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-20T22:18:57+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