M2771491 Mersenne number exponent details

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M2771491

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is 2 ^2771491 - 1

has 834302 decimal digits

takes 0.214 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	91F9E4851A9AD55C	double-checked
PRP	340B7C3E881B5F82	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	21.5064	67.6471%	2700000	84000000	0.7984	7.6827%	22.3049	70.1326%	2.4856%
PrimeNet	2⁵⁹	0.0277	62.7119%	12000	220000	0.0026	2.8565%	0.0303	63.7770%	1.0651%
GPU72	2⁶³	0.5759	65.0794%	15000	240000	0.0031	1.7464%	0.5789	65.6892%	0.6099%
Difference	+5	+20.9306	+2.5677%	+2685000	+83760000	+0.7954	+5.9362%	+21.7260	+4.4434%	+4.4434%

Known prime factors (1 factor, 81.0 bits, 0.00292127% 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
2771491	2356182102899130095261447	25	80.963	425074824868478753 425074824868478753	2020-10-13	1	425074824868478753	95,103	2.594e+9	4.844e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.210%
2010-11-30T00:12:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.606%
2016-08-15T03:12:00	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	3.186%
2016-10-27T01:50:44	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.129%
2016-12-24T02:28:27	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.242%
2017-02-24T04:40:17	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.683%
2017-02-25T21:08:03	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.203%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.014	-	-
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.014	-	-
2016-02-23T16:29:21	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.042	-	-
2009-01-31T07:44:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-19T16:43:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.354	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.708	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.348	-	-
2015-12-06T01:33:44	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.696	-	-
2017-10-12T12:41:22	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.393	-	-
2019-02-24T11:40:38	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.79	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.576 GHz-days
Estimated T-Level:	2.200

Digits	B1	Curves	Complete	FacMiss
20	11000	44 / 100	0.440	64.261%
25	50000	44 / 280	0.157	85.434%

New Calculation Method

Total ECM effort:	4.576 GHz-days
Estimated T-Level:	2.200

Digits	B1	Complete	FacMiss
20	11000	1.419	24.187%
25	50000	0.128	87.961%
30	250000	0.008	99.213%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	4.472
50000	5000000	2356182102899130095261447	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T07:58:00	Aca Arsov	backo6400	50000	5000000						3	0.312
2010-09-22T22:08:00	Kamil_Górski	thefault	50000	5000000						3	0.312
2013-03-08T12:17:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-15T01:48:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-15T13:10:36	Sintax	cloud	50000	5000000						3	0.312
2016-05-21T04:35:33	lettp	Home	50000	5000000						3	0.312
2017-01-23T23:58:07	Ensigma	vps_sing	50000	5000000						3	0.312
2017-08-14T03:24:01	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2018-01-03T20:58:05	Conductor	Andrew	50000	5000000						3	0.312
2018-10-14T23:29:01	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-07T17:18:58	GAN	LMS-08	50000	5000000						3	0.312
2020-08-16T05:27:10	GAN	LMS-15	50000	5000000						3	0.312
2020-09-12T22:48:14	daveward2005	Davy	50000	5000000						7	0.728
2020-10-13T06:34:10	mnd9	kitchen	50000	5000000	2356182102899130095261447	80.963	1	2	2285104416578188	1	0.104

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	91F9E4851A9AD55C	0.214
2018-08-22T18:15:48	kkmrkkblmbrbk	old	91F9E4851A9AD55C	0.214

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-13T15:42:47

mrh.org

2356182102899130095261447

340B7C3E881B5F82

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 294451, B2 = 2944510 (P-1 stage 2)

B1 = 142000, B2 = 4730000 (P-1 stage 2)

B1 = 294451 (P-1 stage 1)

B1 = 110000, B2 = 2365000 (P-1 stage 2)

B1 = 204480 (P-1 stage 1)

B1 = 170400 (P-1 stage 1)

B1 = 142000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

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2⁶⁰

2⁵⁸

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2¹⁰⁰

Last modified: 2020-10-13T15:42:47+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