M6 918 409 Mersenne number exponent details

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M6918409

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is 2 ^6918409 - 1

has 2082649 decimal digits

takes 1.509 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	366C21815E5FE3BC	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	138.2303	68.0556%	4000000	456818670	9.0652	8.0780%	147.2954	70.6360%
Target	2⁶⁷	4.2949	65.6716%	45000	7200000	0.1375	2.2362%	4.4324	66.4393%
Difference	+5	+133.9354	+2.3839%	+3955000	+449618670	+8.9277	+5.8418%	+142.8630	+4.1967%

Known prime factors:
No known factors for M6918409

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22	ANONYMOUS	v4_computers	30000	157500		-		-	-	0.012	-	-	0.580%
2011-09-03	Carsten Kossendey	mother	440000	13310000		-		-	-	0.361	-	-	3.504%
2021-11-12	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.981%
2021-12-02	Seth_Tr	Manual testing	4000000	456818670		-		-	-	9.065	-	-	8.078%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-13	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-09-27	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-11-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-02-12	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		-	-	0.540	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.080	-	-
2016-04-02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.160	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.320	-	-
2020-05-15	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.641	-	-
2021-07-18	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.28	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.56	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.13	-	-

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
2012-09-12	Gerry Snyder	blu	50000	5000000						3	0.995
2017-03-31	mensasnem	thomas	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	0684EE245D63B6__	1.509
1999-12-08	ANONYMOUS	v4_computers	366C21815E5FE3BC	1.509
2002-02-24	ANONYMOUS	v4_computers	366C21815E5FE3BC	1.509

PRP results:
No PRP results for M6918409

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 = 456818670 (P-1 stage 2)

B1 = 3000000, B2 = 75000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 440000, B2 = 13310000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 30000, B2 = 157500 (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: 67.8

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-06-05T21:50:05+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