M6 995 501 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	136.7070	68.0556%	1000000	30000000	0.8157	4.5649%	137.5227	69.5138%
Target	2⁶⁷	4.2476	65.6716%	45000	900000	0.0290	2.2403%	4.2765	66.4407%
Difference	+5	+132.4594	+2.3839%	+955000	+29100000	+0.7868	+2.3246%	+133.2462	+3.0731%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08	ANONYMOUS	v4_computers	30000	202500		-		-	-	0.012	-	-	0.639%
2002-08-03	ANONYMOUS	v4_computers	35000	481250		-		-	-	0.019	-	-	0.891%
2012-08-26	Nesowa	EPC	85000	1530000		-		-	-	0.052	-	-	1.573%
2019-05-07	takahashi	vaio	300000	5000000	6	-		-	-	0.176	-	-	2.686%
2021-07-20	takahashi	vaio	1000000	30000000	12	-		-	-	0.816	-	-	4.565%

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	2⁶²		-	-	0.088	-	-
2005-09-22	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-14	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.534	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.068	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.136	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.273	-	-
2020-04-03	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.546	-	-
2020-07-27	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.09	-	-
2020-09-20	takahashi	Manual testing	2⁷⁰	2⁷¹		-	-	34.18	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.37	-	-

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
2012-09-15	Donna Noble	i3-2100t	50000	5000000						3	0.995
2017-06-07	Benoit Germain	ANN-BGERMAIN	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23	ANONYMOUS	v4_computers	EAD09E4755A76414	1.525
2002-08-24	ANONYMOUS	v4_computers	EAD09E4755A76414	1.525

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 300000, B2 = 5000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 85000, B2 = 1530000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 481250 (P-1 stage 2)

B1 = 30000, B2 = 202500 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

B1 = 30000 (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