M2948977 Mersenne number exponent details

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M2948977

<<<

>>>

is 2 ^2948977 - 1

has 887731 decimal digits

takes 0.251 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	379BE01120553CE3	double-checked
PRP	B83886540A916432	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	20.2121	67.6471%	1000000	20000000	0.2512	5.5435%	20.4632	69.4405%	1.7935%
PrimeNet	2⁵⁹	0.0260	62.7119%	13000	260000	0.0033	3.0734%	0.0293	63.8579%	1.1460%
GPU72	2⁶³	0.5412	65.0794%	17000	300000	0.0040	1.9475%	0.5452	65.7594%	0.6801%
Difference	+5	+19.6708	+2.5677%	+983000	+19700000	+0.2472	+3.5960%	+19.9180	+3.6811%	+3.6811%

Known prime factors (1 factor, 78.9 bits, 0.00267531% 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
2948977	561796189464908944632631	24	78.894	95252724837275595 3 × 5 × 71 × 1027783 × 87021461	2020-09-13	1027783	87021461	25,139	0.7050	1.0928

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.246%
2010-11-03T22:58:00	markr	tiny	95000	1971250		-		-	-	0.024	-	-	2.449%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	116765	116765		-		-	-	0.014	-	-	0.928%
2015-01-26T12:23:00	Jocelyn Larouche	Manual testing	141285	141285		-		-	-	0.017	-	-	1.032%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	170954	170954		-		-	-	0.021	-	-	1.144%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	188049	188049		-		-	-	0.023	-	-	1.202%
2015-02-03T07:46:00	Jocelyn Larouche	Manual testing	206853	206853		-		-	-	0.026	-	-	1.262%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	366450	366450		-		-	-	0.045	-	-	1.661%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	403095	403095		-		-	-	0.050	-	-	1.734%
2015-02-23T15:50:00	Jocelyn Larouche	Manual testing	443404	443404		-		-	-	0.055	-	-	1.809%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	536518	536518		-		-	-	0.066	-	-	1.964%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	590169	590169		-		-	-	0.073	-	-	2.044%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	785513	785513		-		-	-	0.097	-	-	2.296%
2015-04-29T15:00:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.544%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:25	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-14T05:44:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-14T05:25:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.333	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.666	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.267	-	-
2016-02-25T09:22:06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.534	-	-
2017-11-28T10:01:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.068	-	-
2018-12-24T00:53:32	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.14	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.432 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	2.432 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	2.084
50000	5000000	561796189464908944632631	3	0.347

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-01T04:17:00	James Hintz	15_061809	50000	5000000						3	0.347
2011-04-19T20:29:00	Pool Party	desk_1	50000	5000000						3	0.347
2013-07-04T20:48:00	Bruce	fx6840-21	50000	5000000						3	0.347
2016-01-01T14:57:58	Bruce	Desk7	50000	5000000						3	0.347
2017-06-05T13:02:09	Bruce	Desk10	50000	5000000						3	0.347
2019-10-04T23:08:50	Claude Portenier	Petit-Idiot	50000	5000000						3	0.347
2020-09-13T11:54:35	MarkS	desktop-i7	50000	5000000	561796189464908944632631	78.894	3	2	6551612102154086	3	0.347

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-01T00:00:00	ANONYMOUS	v4_computers	379BE01120553CE3	0.251
1999-05-30T00:00:00	ANONYMOUS	v4_computers	379BE01120553CE3	0.251
2000-04-27T00:00:00	ANONYMOUS	v4_computers	379BE01120553CE3	0.251
2018-10-12T07:43:19	kkmrkkblmbrbk	old	379BE01120553CE3	0.251

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-16T12:52:47

ViliamF

AWS

561796189464908944632631

B83886540A916432

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 785513 (P-1 stage 1)

B1 = 590169 (P-1 stage 1)

B1 = 536518 (P-1 stage 1)

B1 = 443404 (P-1 stage 1)

B1 = 403095 (P-1 stage 1)

B1 = 366450 (P-1 stage 1)

B1 = 206853 (P-1 stage 1)

B1 = 95000, B2 = 1971250 (P-1 stage 2)

B1 = 188049 (P-1 stage 1)

B1 = 170954 (P-1 stage 1)

B1 = 141285 (P-1 stage 1)

B1 = 116765 (P-1 stage 1)

B1 = 95000 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-09-16T12:52:47+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