M6 378 517 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	149.9304	68.0556%	4000000	18004726740	253.0481	12.0521%	402.9785	71.9055%
Target	2⁶⁶	2.3153	65.1515%	45000	8000000	0.1229	2.5712%	2.4383	66.0476%
Difference	+6	+147.6151	+2.9040%	+3955000	+17996726740	+252.9251	+9.4808%	+400.5402	+5.8580%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6378517	289786424583786562100408335507799514673	39	127.768	22715815022816946486182316007608 2³ × 3 × 29² × 283 × 22157 × 74047 × 1096031 × 2211532811	2023-04-24	1096031	2211532811	2.624e+10	31.229	57.830

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-04	ANONYMOUS	v4_computers	30000	435000		-		-	-	0.013	-	-	0.807%
2014-10-18	Nesowa	newfs	390000	9750000		-		-	-	0.231	-	-	3.196%
2022-10-06	takahashi	vaio	2500000	50028510		-		-	-	1.308	-	-	5.437%
2023-04-19	linament	U2K	3999900	3999900		-		-	-	1.028	-	-	3.014%
2023-04-24	linament	Cyber	4000000	18004726740			289786424583786562100408335507799514673	39	127.768	253.0	2.261	506.1	12.052%

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		-	-	0.096	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.154	-	-
2014-08-17	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.308	-	-
2014-08-20	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.586	-	-
2015-10-21	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.172	-	-
2016-04-08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.343	-	-
2018-06-04	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.686	-	-
2020-05-05	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.372	-	-
2021-02-11	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	18.74	-	-
2022-01-02	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	37.49	-	-
2022-07-31	takahashi	Manual testing	2⁷¹	2⁷²		-	-	74.98	-	-

ECM factoring results:

Total ECM effort:	1.617 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	1.617

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-11-29	Piepen	T41-2000	50000	5000000						3	0.808
2016-10-13	fireredd	ont1	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	Paul Victor Novarese	gilligan	3F7CEE06F79F111D	1.130
1999-09-14	curtisc	v4_computers	3F7CEE06F79F111D	1.130

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 = 18004726740 (P-1 stage 2)

B1 = 2500000, B2 = 50028510 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3999900 (P-1 stage 1)

B1 = 2500000 (P-1 stage 1)

B1 = 390000, B2 = 9750000 (P-1 stage 2)

B1 = 390000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 66

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