M3195331 Mersenne number exponent details

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M3195331

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>>>

is 2 ^3195331 - 1

has 961891 decimal digits

takes 0.272 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	0A05F954B35FC065	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	37.3629	68.1159%	4000000	150000000	1.4753	8.0974%	38.8382	70.6977%	2.5818%
PrimeNet	2⁶⁰	0.0481	63.3333%	13000	240000	0.0031	2.6567%	0.0512	64.3075%	0.9741%
GPU72	2⁶⁴	1.1139	65.6250%	16000	260000	0.0036	1.6153%	1.1175	66.1802%	0.5552%
Difference	+5	+36.2490	+2.4909%	+3984000	+149740000	+1.4717	+6.4822%	+37.7207	+4.5175%	+4.5175%

Known prime factors (1 factor, 71.4 bits, 0.00223410% 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
3195331	3087129632822960277617	22	71.387	483068832747368 2³ × 7 × 13367 × 645337709	2021-10-04	13367	645337709	227.63	4.3407	8.1042

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.203%
2013-01-08T01:34:00	Squeeky_Squirrel	T7500_2200	215000	6235000		-		-	-	0.067	-	-	3.316%
2018-09-04T00:51:13	Jocelyn Larouche	low 4M	520300	1040600		-		-	-	0.068	-	-	2.289%
2018-09-04T09:57:14	Jocelyn Larouche	low 4M	520300	1560900		-		-	-	0.071	-	-	2.612%
2018-09-04T22:49:15	Jocelyn Larouche	low 4M	520300	2081200		-		-	-	0.075	-	-	2.844%
2018-09-05T10:15:27	Jocelyn Larouche	low 4M	520300	2601500		-		-	-	0.078	-	-	3.025%
2018-09-07T07:56:54	Jocelyn Larouche	low 4M	520300	4162400		-		-	-	0.089	-	-	3.410%
2019-11-19T04:58:12	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.097%
2022-03-10T20:59:50	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	6.997%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-07T05:38:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-12T09:15:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.307	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.614	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.169	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.339	-	-
2017-05-01T03:37:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.677	-	-
2018-12-17T13:21:56	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.355	-	-
2021-07-22T10:09:29	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	18.71	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.220 GHz-days
Estimated T-Level:	3.500

Digits	B1	Curves	Complete	FacMiss
20	11000	70 / 100	0.700	49.484%
25	50000	70 / 280	0.250	77.845%

New Calculation Method

Total ECM effort:	8.220 GHz-days
Estimated T-Level:	3.500

Digits	B1	Complete	FacMiss
20	11000	2.258	10.455%
25	50000	0.204	81.540%
30	250000	0.013	98.751%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		64	7.516
50000	5000000	3087129632822960277617	6	0.705

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-07T05:08:00	TeamResslerTUB	1062320	50000	5000000						3	0.352
2011-09-07T06:09:00	sannerud.com	Jens2010	50000	5000000						3	0.352
2014-04-15T16:51:00	Bruce	fx6840-21	50000	5000000						3	0.352
2016-07-17T20:33:28	f0rteOC	Fortissimo	50000	5000000						3	0.352
2018-07-19T22:32:13	IanGlencross	glenx24	50000	5000000						3	0.352
2020-12-19T09:15:47	Zenzoma	AMD3970X	50000	5000000						7	0.822
2021-01-24T22:35:47	mnd9	office2	50000	5000000						7	0.822
2021-02-18T23:32:56	GAN	KL-SCH01	50000	5000000						7	0.822
2021-03-20T20:02:09	mnd9	27016b	50000	5000000						7	0.822
2021-05-04T03:35:24	daveward2005	Dave2	50000	5000000						7	0.822
2021-06-18T23:57:31	C.D.B.	i7-6850K	50000	5000000						7	0.822
2021-07-30T15:27:09	daveward2005	Davy	50000	5000000						7	0.822
2021-10-04T01:34:15	GAN	KL-SCH07	50000	5000000	3087129632822960277617	71.387	6	2	7989276145668765	6	0.705

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-01-25T00:00:00	ANONYMOUS	v4_computers	F1B76AC17F7BB6__	0.272

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-06T03:19:37

GAN

LMS-11

3087129632822960277617

0A05F954B35FC065

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 = 134343300 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 520300, B2 = 4162400 (P-1 stage 2)

B1 = 520300, B2 = 2601500 (P-1 stage 2)

B1 = 520300, B2 = 2081200 (P-1 stage 2)

B1 = 520300, B2 = 1560900 (P-1 stage 2)

B1 = 520300, B2 = 1040600 (P-1 stage 2)

B1 = 215000, B2 = 6235000 (P-1 stage 2)

B1 = 520300 (P-1 stage 1)

B1 = 215000 (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:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-10T20:59:50+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