M3164081 Mersenne number exponent details

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is 2 ^3164081 - 1

has 952484 decimal digits

takes 0.269 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	F4AEAE55C20C07A5	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	37.7319	68.1159%	3000000	100000000	1.0224	7.4334%	38.7543	70.4860%	2.3701%
PrimeNet	2⁶⁰	0.0485	63.3333%	13000	240000	0.0031	2.6520%	0.0517	64.3057%	0.9724%
GPU72	2⁶⁴	1.1249	65.6250%	15000	260000	0.0035	1.5813%	1.1284	66.1686%	0.5436%
Difference	+5	+36.6070	+2.4909%	+2985000	+99740000	+1.0189	+5.8521%	+37.6259	+4.3174%	+4.3174%

Known prime factors:
No known factors for M3164081

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	-	-	0.203%
2009-07-03T00:42:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.666%
2011-09-09T08:46:00	Squeeky_Squirrel	T7500_2200	60000	960000		-		-	-	0.013	-	-	1.648%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	80285	80285		-		-	-	0.010	-	-	0.650%
2014-09-25T21:11:00	Jocelyn Larouche	Manual testing	100570	100570		-		-	-	0.012	-	-	0.748%
2015-08-10T13:57:00	Jocelyn Larouche	Manual testing	433983	433983		-		-	-	0.054	-	-	1.607%
2015-11-05T00:02:31	Jocelyn Larouche	Manual testing	552156	552156		-		-	-	0.068	-	-	1.788%
2015-11-28T03:20:19	HBendtz	Manual testing	500000	12000000	12	-		-	-	0.139	-	-	4.271%
2019-07-19T02:34:37	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	7.433%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-10T19:14:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-10-28T22:13:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.097	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.310	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.620	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.181	-	-
2015-06-17T10:00:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.362	-	-
2017-04-22T18:10:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.723	-	-
2019-01-21T12:54:07	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.447	-	-
2021-06-14T11:22:14	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	18.89	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.883 GHz-days
Estimated T-Level:	4.600

Digits	B1	Curves	Complete	FacMiss
20	11000	92 / 100	0.920	39.668%
25	50000	92 / 280	0.329	71.953%

New Calculation Method

Total ECM effort:	10.883 GHz-days
Estimated T-Level:	4.600

Digits	B1	Complete	FacMiss
20	11000	3.549	2.875%
25	50000	0.329	71.964%
30	250000	0.021	97.945%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		85	9.96
50000	6350000		7	0.919

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	LEE Sau Dan	v4_computers	F4AEAE55C20C07A5	0.269
1999-12-08T00:00:00	ANONYMOUS	v4_computers	F4AEAE55C20C07A5	0.269

PRP results:
No PRP results for M3164081

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 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 12000000 (P-1 stage 2)

B1 = 552156 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 433983 (P-1 stage 1)

B1 = 60000, B2 = 960000 (P-1 stage 2)

B1 = 100570 (P-1 stage 1)

B1 = 80285 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (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

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10⁸

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-06-03T02:20:50+00:00