M6 973 831 Mersenne number exponent details

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M6973831

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is 2 ^6973831 - 1

has 2099333 decimal digits

takes 1.521 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	E326AA612657C3AD	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	137.1318	68.0556%	2000000	258849360	5.0569	6.9834%	142.1887	70.2864%
Target	2⁶⁷	4.2608	65.6716%	45000	900000	0.0290	2.2392%	4.2897	66.4403%
Difference	+5	+132.8710	+2.3839%	+1955000	+257949360	+5.0280	+4.7442%	+137.8990	+3.8460%

Known prime factors:
No known factors for M6973831

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-16	ANONYMOUS	v4_computers	35000	288750		-		-	-	0.015	-	-	0.757%
2011-12-07	James Heinrich	Q6600	135000	2835000		-		-	-	0.089	-	-	2.034%
2020-01-28	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.585%
2021-12-07	Seth_Tr	Manual testing	2000000	258849360		-		-	-	5.057	-	-	6.983%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-11	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2004-03-26	Sturle Sunde	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.282	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.536	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.072	-	-
2016-04-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.143	-	-
2018-02-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.286	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.572	-	-
2021-08-07	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.14	-	-
2021-09-06	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.29	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.58	-	-

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
2012-09-06	kracker		50000	5000000						3	0.995
2012-09-06	kracker	Manual testing	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14	ANONYMOUS	v4_computers	E326AA612657C3AD	1.521
2001-12-22	ANONYMOUS	v4_computers	E326AA612657C3AD	1.521

PRP results:
No PRP results for M6973831

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

B1 = 600000 (P-1 stage 1)

B1 = 135000, B2 = 2835000 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

B1 = 35000, B2 = 288750 (P-1 stage 2)

B1 = 35000 (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