M6 958 031 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.4431	68.0556%	600000	12000000	0.3861	3.5839%	137.8292	69.2004%
Target	2⁶⁷	4.2704	65.6716%	45000	900000	0.0290	2.2383%	4.2994	66.4400%
Difference	+5	+133.1727	+2.3839%	+555000	+11100000	+0.3571	+1.3456%	+133.5298	+2.7604%

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	35000	288750		-		-	-	0.015	-	-	0.756%
2011-12-11	James Heinrich	Q6600	130000	2827500		-		-	-	0.088	-	-	2.016%
2020-01-23	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.584%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11	Kimon Berlin	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-07-17	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.282	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.537	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.074	-	-
2016-04-06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.148	-	-
2018-02-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.296	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.592	-	-
2021-08-01	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.18	-	-
2021-08-17	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.37	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.73	-	-

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
2012-09-03	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-06-27	Benoit Germain	ANN-BGERMAIN	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	437A8E04F5B3B329	1.517
2001-10-13	ANONYMOUS	v4_computers	437A8E04F5B3B329	1.517

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

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2827500 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

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

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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

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