M7 631 251 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	2⁷³	250.6593	68.4932%	3000000	9477604500	164.1618	10.4242%	414.8211	71.7775%
Target	2⁶⁷	3.8937	65.6716%	50000	1100000	0.0339	2.4442%	3.9276	66.5107%
Difference	+6	+246.7656	+2.8215%	+2950000	+9476504500	+164.1279	+7.9800%	+410.8935	+5.2668%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7631251	1924091056017399437570204031985285007969	40	130.499	126066555537054110628139739603984 2⁴ × 7² × 13381 × 40849 × 406361 × 567493 × 1275678673	2023-02-17	567493	1275678673	2.105e+10	22.145	41.044

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03	ANONYMOUS	v4_computers	35000	35000		-		-	-	0.011	-	-	0.229%
2011-04-16	James Heinrich	Q6600	145000	3190000		-		-	-	0.098	-	-	1.913%
2023-02-17	DRobinsonPE	5600X	3000000	9477604500			1924091056017399437570204031985285007969	40	130.499	164.2	3.328	328.3	10.424%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-24	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.209	-	-
2013-10-11	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.257	-	-
2013-12-04	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.490	-	-
2015-06-09	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.979	-	-
2016-09-14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	1.958	-	-
2018-07-31	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	3.917	-	-
2020-03-06	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	7.834	-	-
2021-04-07	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	15.67	-	-
2021-04-07	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	31.34	-	-
2021-04-21	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	62.67	-	-
2021-04-21	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	125.3	-	-

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
2012-12-31	Florimond C.	arm.durga	50000	5000000						3	0.995
2018-05-02	arnaud	snd-15-157	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-26	Stephen Wood	v4_computers	10887A65A4CE55AA	1.664
2002-12-09	ANONYMOUS	v4_computers	10887A65A4CE55AA	1.664

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 = 3000000, B2 = 9477604500 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 145000, B2 = 3190000 (P-1 stage 2)

B1 = 145000 (P-1 stage 1)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

this exponent TF target: 67

TF double-checked to: 67.7

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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