M3331837 Mersenne number exponent details

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M3331837

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is 2 ^3331837 - 1

has 1002983 decimal digits

takes 0.350 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	6BCA3B7BF27CFE3B	double-checked
PRP	1D414BD3D020F7CC	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	17.8895	67.6471%	4000000	150000000	1.8206	8.7944%	19.7100	70.4923%	2.8452%
PrimeNet	2⁶⁰	0.0461	63.3333%	14000	260000	0.0042	2.7832%	0.0503	64.3538%	1.0205%
GPU72	2⁶⁴	1.0683	65.6250%	18000	300000	0.0051	1.7536%	1.0734	66.2278%	0.6028%
Difference	+4	+16.8212	+2.0221%	+3982000	+149700000	+1.8155	+7.0408%	+18.6367	+4.2645%	+4.2645%

Known prime factors (1 factor, 72.9 bits, 0.00218691% 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
3331837	8597427533580012097513	22	72.864	1290193297808388 2² × 3 × 107516108150699	2021-06-09	4	107516108150699	357.12	892,082	1,666,161

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:40:00	Carsten Kossendey	durandal	15000	202500		-		-	-	0.004	-	-	0.804%
2011-10-06T05:08:00	harlee	P4_2600	55000	880000		-		-	-	0.015	-	-	1.812%
2012-11-24T00:54:00	Squeeky_Squirrel	P4_2600	210000	4672500		-		-	-	0.069	-	-	3.481%
2018-08-07T17:09:37	Jocelyn Larouche	low 4M	420000	840000		-		-	-	0.067	-	-	2.365%
2018-08-15T10:51:07	Jocelyn Larouche	low 4M	420000	2940000		-		-	-	0.085	-	-	3.415%
2018-08-16T10:37:55	Jocelyn Larouche	low 4M	420000	3360000		-		-	-	0.088	-	-	3.529%
2020-05-31T10:52:40	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.794%
2022-04-02T19:48:47	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.663%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-17T00:00:00	Trent Taufer	v4_computers	2¹	2⁶⁰		-	-	0.046	-	-
2009-03-30T15:06:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-09-01T20:36:00	markr	Manual testing	2¹	2⁶²		-	-	0.184	-	-
2012-08-25T21:54:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.479	-	-
2016-02-23T16:29:26	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.295	-	-
2015-02-11T09:06:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.589	-	-
2015-02-11T09:06:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.121	-	-
2016-03-02T03:51:55	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.243	-	-
2017-02-28T14:37:41	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.486	-	-
2018-11-12T14:47:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.971	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.549 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	5.549 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.226	29.352%
25	50000	0.111	89.513%
30	250000	0.007	99.320%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.257
50000	5000000	8597427533580012097513	2	0.292

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-31T15:50:00	TeamResslerTUB	1062314	50000	5000000						3	0.438
2011-11-13T03:43:00	kracker	A8-PC	50000	5000000						3	0.438
2014-09-30T19:32:00	PageFault	Manual testing	50000	5000000						9	1.314
2021-02-09T03:52:12	C.D.B.	i7-6850K	50000	5000000						7	1.022
2021-04-17T02:45:57	Denis Porva	Yrok	50000	5000000						7	1.022
2021-05-19T17:38:47	Claude Portenier	Petit-Idiot	50000	5000000						7	1.022
2021-06-09T01:31:55	daveward2005	d12436	50000	5000000	8597427533580012097513	72.864	2	2	3673078354559814	2	0.292

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-01T00:00:00	Trent Taufer	v4_computers	6BCA3B7BF27CFE3B	0.350
1999-11-10T00:00:00	ANONYMOUS	v4_computers	6BCA3B7BF27CFE3B	0.350

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-06-10T03:08:29

Chang Chia-Tche

homura

8597427533580012097513

1D414BD3D020F7CC

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 = 420000, B2 = 3360000 (P-1 stage 2)

B1 = 420000, B2 = 2940000 (P-1 stage 2)

B1 = 210000, B2 = 4672500 (P-1 stage 2)

B1 = 420000, B2 = 840000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 210000 (P-1 stage 1)

B1 = 55000, B2 = 880000 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 202500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:47+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