M6 908 813 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	138.4223	68.0556%	4000000	456818670	9.0652	8.0769%	147.4874	70.6357%
Target	2⁶⁷	4.3009	65.6716%	45000	900000	0.0290	2.2357%	4.3298	66.4391%
Difference	+5	+134.1214	+2.3839%	+3955000	+455918670	+9.0362	+5.8412%	+143.1576	+4.1966%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-31	BJB	v4_computers	35000	542500		-		-	-	0.020	-	-	0.921%
2012-08-11	Nesowa	EPC	85000	1487500		-		-	-	0.051	-	-	1.559%
2018-03-15	Squeeky_Squirrel	i5-5250U_1600	405000	12251250	12	-		-	-	0.332	-	-	3.404%
2021-11-18	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.981%
2021-11-30	Seth_Tr	Manual testing	4000000	456818670		-		-	-	9.065	-	-	8.077%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-07-01	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-18	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.541	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.082	-	-
2016-04-01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.163	-	-
2018-05-23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.326	-	-
2019-12-11	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.653	-	-
2020-12-21	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.31	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.61	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.22	-	-

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
2012-08-19	Gerry Snyder	blu	50000	5000000						3	0.995
2017-03-27	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26	ANONYMOUS	v4_computers	3486786D4826E942	1.507
2001-08-31	BJB	v4_computers	3486786D4826E942	1.507

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 = 405000, B2 = 12251250 (P-1 stage 2)

B1 = 405000 (P-1 stage 1)

B1 = 85000, B2 = 1487500 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 542500 (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

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