M8 037 151 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	118.9891	68.0556%	3000000	4532960250	94.5788	10.4521%	213.5680	71.3944%
Target	2⁶⁷	3.6971	65.6716%	55000	6000000	0.1435	2.5687%	3.8405	66.5534%
Difference	+5	+115.2921	+2.3839%	+2945000	+4526960250	+94.4354	+7.8834%	+209.7275	+4.8410%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8037151	255783430448377947449030602301852623961	39	127.588	15912568424332076593374356304980 2² × 5 × 13 × 23 × 163 × 3617 × 8039 × 56711 × 1365577 × 7249657	2022-11-27	1365577	7249657	2.234e+10	0.6384	1.0522

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-07-14	ANONYMOUS	v4_computers	45000	731250		-		-	-	0.031	-	-	1.114%
2002-11-16	ANONYMOUS	v4_computers	45000	731250		-		-	-	0.031	-	-	1.114%
2002-12-16	ANONYMOUS	v4_computers	45000	731250		-		-	-	0.031	-	-	1.114%
2012-10-05	Nesowa	EPC	100000	1950000		-		-	-	0.076	-	-	1.778%
2020-11-14	Dylan Delgado	Manual testing	500000	16000000	12	-		-	-	0.509	-	-	3.772%
2022-11-26	linament	colab	2999900	2999900		-		-	-	1.136	-	-	2.817%
2022-11-27	linament	U2K	3000000	4532960250			255783430448377947449030602301852623961	39	127.588	94.58	4.197	189.2	10.452%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.076	-	-
1999-02-07	Phillip Remaker	v4_computers	2¹	2⁶³		-	-	0.199	-	-
2013-08-25	David Campeau	Manual testing	2⁶³	2⁶⁴		-	-	0.244	-	-
2013-12-24	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.465	-	-
2015-04-24	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	0.930	-	-
2015-11-18	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.860	-	-
2017-09-11	Sid & Andy	Manual testing	2⁶⁷	2⁶⁸		-	-	3.719	-	-
2020-02-07	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	7.438	-	-
2021-03-14	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	14.88	-	-
2021-03-14	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	29.75	-	-
2021-03-14	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	59.51	-	-

ECM factoring results:

Total ECM effort:	2.382 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	2.382

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-02-12	Florimond C.	arm.durga	50000	5000000						3	1.191
2018-12-19	arnaud	snd-15-157	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-31	ANONYMOUS	v4_computers	10BC2FEB3500D229	2.099
2002-07-14	ANONYMOUS	v4_computers	10BC2FEB3500D229	2.099
2002-11-16	ANONYMOUS	v4_computers	10BC2FEB3500D229	2.099
2002-12-16	ANONYMOUS	v4_computers	10BC2FEB3500D229	2.099

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 = 4532960250 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2999900 (P-1 stage 1)

B1 = 500000, B2 = 16000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 100000, B2 = 1950000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 45000, B2 = 731250 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.9

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