M6 976 441 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	137.0804	68.0556%	2000000	58000000	1.5970	5.5228%	138.6775	69.8198%
Target	2⁶⁷	4.2592	65.6716%	45000	900000	0.0290	2.2393%	4.2881	66.4404%
Difference	+5	+132.8213	+2.3839%	+1955000	+57100000	+1.5681	+3.2835%	+134.3893	+3.3794%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-29	ANONYMOUS	v4_computers	75000	937500		-		-	-	0.039	-	-	1.336%
2001-10-20	ANONYMOUS	v4_computers	35000	341250		-		-	-	0.016	-	-	0.800%
2014-08-17	Nesowa	newfs	435000	11418750		-		-	-	0.327	-	-	3.396%
2021-11-05	Seth_Tr	Manual testing	2000000	58000000	12	-		-	-	1.597	-	-	5.523%

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	-	-
2000-04-05	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.536	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.071	-	-
2016-04-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.142	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.285	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.569	-	-
2021-08-08	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.14	-	-
2021-09-07	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.28	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.55	-	-

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
2012-09-08	Donna Noble	i3-2100t	50000	5000000						3	0.995
2017-05-07	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23	ANONYMOUS	v4_computers	685DBF2BE18ACD__	1.521
2000-07-25	ANONYMOUS	v4_computers	B17983E583E56824	1.521
2001-11-03	ANONYMOUS	v4_computers	B17983E583E56824	1.521

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 = 58000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 435000, B2 = 11418750 (P-1 stage 2)

B1 = 435000 (P-1 stage 1)

B1 = 75000, B2 = 937500 (P-1 stage 2)

B1 = 75000 (P-1 stage 1)

B1 = 35000, B2 = 341250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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