M7 313 759 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	130.7582	68.0556%	3200000	10807226430	187.1261	11.3756%	317.8843	71.6894%
Target	2⁶⁷	4.0627	65.6716%	45000	1000000	0.0307	2.3164%	4.0934	66.4668%
Difference	+5	+126.6954	+2.3839%	+3155000	+10806226430	+187.0955	+9.0591%	+313.7909	+5.2226%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7313759	53637367576323142592479	23	75.506	3666880982564721 3² × 19 × 101 × 157 × 1352320643	2023-01-29	157	1352320643	1,377.1	23.296	43.510
7313759	641071103517349056219305183797100546401	39	128.914	43826375979667162687429622974800 2⁴ × 3 × 5² × 11 × 19² × 5393 × 488779 × 1292783 × 2698894049	2023-01-29	1292783	2698894049	2.131e+10	46.879	86.834

exponent	prime factors	composite factor	digits	bits*
7313759	53637367576323142592479 641071103517349056219305183797100546401	34385366421919155199885530560227591605801159549663 446573118079	62	204.419

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-28	ANONYMOUS	v4_computers	35000	262500		-		-	-	0.015	-	-	0.739%
2012-03-03	David Campeau	i5-work	115000	2271250		-		-	-	0.074	-	-	1.876%
2021-10-06	Architects Cubed	bmlt	256000	10821000		-		-	-	0.263	-	-	3.103%
2023-01-29	DRobinsonPE	5700G	3200000	10807226430			53637367576323142592479 641071103517349056219305183797100546401	62	204.419	187.1	3.190	374.3	11.376%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.218	-	-
2013-10-28	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.268	-	-
2013-11-18	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.511	-	-
2015-06-21	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.022	-	-
2016-10-04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.043	-	-
2018-08-05	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.087	-	-
2020-10-18	GdS	Manual testing	2⁶⁸	2⁶⁹		-	-	8.174	-	-
2020-10-18	GdS	Manual testing	2⁶⁹	2⁷⁰		-	-	16.35	-	-
2020-10-18	GdS	Manual testing	2⁷⁰	2⁷¹		-	-	32.70	-	-
2021-10-13	SRBase	Manual testing	2⁷¹	2⁷²		-	-	65.39	-	-

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
2012-11-21	Donna Noble	opt4820	50000	5000000						3	0.995
2017-12-22	Yan Jinzhao	baidupaid	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-22	ANONYMOUS	v4_computers	332E308BD6CAE122	1.595
1999-12-08	ANONYMOUS	v4_computers	A396F8BD205B0C79	1.595
2002-03-16	ANONYMOUS	v4_computers	A396F8BD205B0C79	1.595

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 = 3200000, B2 = 10807226430 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 256000, B2 = 10821000 (P-1 stage 2)

B1 = 256000 (P-1 stage 1)

B1 = 115000, B2 = 2271250 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 35000, B2 = 262500 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

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

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