M6 995 137 Mersenne number exponent details

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M6995137

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is 2 ^6995137 - 1

has 2105747 decimal digits

takes 1.525 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	88D7CC632B53068D	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	136.7141	68.0556%	2500000	50000000	1.6087	5.4904%	138.3228	69.8094%
Target	2⁶⁷	4.2478	65.6716%	45000	900000	0.0290	2.2403%	4.2768	66.4407%
Difference	+5	+132.4663	+2.3839%	+2455000	+49100000	+1.5797	+3.2501%	+134.0460	+3.3687%

Known prime factors:
No known factors for M6995137

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-22	ANONYMOUS	v4_computers	30000	30000		-		-	-	0.009	-	-	0.235%
2002-03-16	ANONYMOUS	v4_computers	80000	1420000		-		-	-	0.048	-	-	1.520%
2019-03-06	takahashi	vaio	250000	4400000	6	-		-	-	0.151	-	-	2.532%
2020-12-24	takahashi	vaio	2500000	50000000	12	-		-	-	1.609	-	-	5.490%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11	WanderingShoe	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2000-12-14	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-09-22	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-14	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.534	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.068	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.137	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.273	-	-
2020-04-03	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.546	-	-
2020-07-27	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.09	-	-
2020-09-20	takahashi	Manual testing	2⁷⁰	2⁷¹		-	-	34.18	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.37	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-27	alan145	Bear4	50000	5000000						3	0.995
2017-05-18	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Brian J. Beesley	cabbage	88D7CC632B53068D	1.525
1999-04-13	ANONYMOUS	v4_computers	41C126EFC3F209__	1.525
1999-07-04	ANONYMOUS	v4_computers	88D7CC632B53068D	1.525

PRP results:
No PRP results for M6995137

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 = 2500000, B2 = 50000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 250000, B2 = 4400000 (P-1 stage 2)

B1 = 250000 (P-1 stage 1)

B1 = 80000, B2 = 1420000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-04-26T21:34:10+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