M6 902 741 Mersenne number exponent details

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M6902741

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is 2 ^6902741 - 1

has 2077933 decimal digits

takes 1.505 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	14B3DBD4E26122B6	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	138.5440	68.0556%	4000000	414323910	8.3331	7.9694%	146.8772	70.6013%
Target	2⁶⁷	4.3047	65.6716%	45000	900000	0.0290	2.2354%	4.3336	66.4390%
Difference	+5	+134.2394	+2.3839%	+3955000	+413423910	+8.3042	+5.7340%	+142.5436	+4.1623%

Known prime factors:
No known factors for M6902741

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-26	ANONYMOUS	v4_computers	30000	270000		-		-	-	0.014	-	-	0.704%
2011-11-19	James Heinrich	i7-920	130000	2665000		-		-	-	0.085	-	-	1.985%
2020-01-07	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.580%
2021-11-20	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.529%
2021-11-29	Seth_Tr	Manual testing	4000000	414323910		-		-	-	8.333	-	-	7.969%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-29	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.045	-	-
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-01-20	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-17	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.541	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.083	-	-
2016-03-31	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.165	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.330	-	-
2019-11-27	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.661	-	-
2020-12-20	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.32	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.64	-	-
2021-10-10	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.28	-	-

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
2012-08-11	Clown_Royal	lab	50000	5000000						3	0.995
2017-03-24	h0b0byter99	camserve	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15	ANONYMOUS	v4_computers	BA4C7F35EC9C58__	1.505
1999-06-26	ANONYMOUS	v4_computers	14B3DBD4E26122B6	1.505
2001-12-01	ANONYMOUS	v4_computers	14B3DBD4E26122B6	1.505

PRP results:
No PRP results for M6902741

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 = 414323910 (P-1 stage 2)

B1 = 4000000, B2 = 110000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2665000 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 30000, B2 = 270000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-03-23T17:39:31+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