M6 926 587 Mersenne number exponent details

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M6926587

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is 2 ^6926587 - 1

has 2085111 decimal digits

takes 1.510 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	1A4E9D19551C92B1	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	138.0671	68.0556%	2000000	258849360	5.0569	6.9785%	143.1240	70.2848%
Target	2⁶⁷	4.2898	65.6716%	45000	900000	0.0290	2.2366%	4.3188	66.4394%
Difference	+5	+133.7772	+2.3839%	+1955000	+257949360	+5.0280	+4.7419%	+138.8052	+3.8454%

Known prime factors:
No known factors for M6926587

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-10-20	ANONYMOUS	v4_computers	30000	30000		-		-	-	0.009	-	-	0.234%
2011-09-03	Carsten Kossendey	mother	440000	13310000		-		-	-	0.361	-	-	3.505%
2021-06-02	Dylan Delgado	Manual testing	630000	18900000	12	-		-	-	0.514	-	-	3.947%
2021-12-06	Seth_Tr	Manual testing	2000000	258849360		-		-	-	5.057	-	-	6.978%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-02-18	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-17	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.539	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.079	-	-
2016-04-03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.158	-	-
2018-05-23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.315	-	-
2020-05-01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.631	-	-
2021-07-22	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.26	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.52	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.05	-	-

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
2012-08-21	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-04-04	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	E68C731CF0DC70__	1.510
2000-06-11	ANONYMOUS	v4_computers	1A4E9D19551C92B1	1.510
2001-11-10	ANONYMOUS	v4_computers	1A4E9D19551C92B1	1.510

PRP results:
No PRP results for M6926587

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 = 2000000, B2 = 258849360 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 630000, B2 = 18900000 (P-1 stage 2)

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

B1 = 630000 (P-1 stage 1)

B1 = 440000 (P-1 stage 1)

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