M6 351 809 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	150.5608	68.0556%	4000000	18004726740	253.0481	12.0479%	403.6089	71.9042%
Target	2⁶⁶	2.3251	65.1515%	45000	5000000	0.0809	2.5695%	2.4060	66.0469%
Difference	+6	+148.2358	+2.9040%	+3955000	+17999726740	+252.9671	+9.4784%	+401.2029	+5.8572%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6351809	357629800375982805907879	24	78.243	28151806861319571 3² × 19 × 962237 × 171091373	2023-04-03	962237	171091373	12,623	2.6292	4.4739
6351809	1132845877868291721291871011748754746231	40	129.735	89175058465099605584162796122235 3 × 5 × 1549 × 1933 × 79691 × 116681 × 816811 × 261419437	2023-04-03	816811	261419437	2.077e+10	3.8585	6.8359

exponent	prime factors	composite factor	digits	bits*
6351809	357629800375982805907879 1132845877868291721291871011748754746231	40513944515879216644936229624028751647387061082044 2268208454049	63	207.978

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-04-21	ANONYMOUS	v4_computers	30000	352500		-		-	-	0.012	-	-	0.756%
2014-10-09	Nesowa	newfs	385000	9721250		-		-	-	0.230	-	-	3.186%
2022-09-09	takahashi	vaio	2500000	50028510		-		-	-	1.308	-	-	5.434%
2023-04-02	linament	U2K	3999900	3999900		-		-	-	1.028	-	-	3.013%
2023-04-03	linament	Cyber	4000000	18004726740			357629800375982805907879 1132845877868291721291871011748754746231	63	207.978	253.0	2.251	506.1	12.048%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-28	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.097	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.155	-	-
2014-08-17	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.309	-	-
2014-08-21	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.588	-	-
2015-10-20	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.176	-	-
2016-04-02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.353	-	-
2018-06-04	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.706	-	-
2020-04-30	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.412	-	-
2021-02-07	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	18.82	-	-
2021-12-26	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	37.65	-	-
2022-06-17	takahashi	Manual testing	2⁷¹	2⁷²		-	-	75.29	-	-

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
2011-11-14	Sid & Andy	Bo_Peep	50000	5000000						3	0.808
2016-09-25	William Labbett	john	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	Dylan Jones	v4_computers	F568D4A1AF55A0__	1.126
1999-07-26	ANONYMOUS	v4_computers	B42B54D678D3E2F2	1.126
2001-06-17	ANONYMOUS	v4_computers	B42B54D678D3E2F2	1.126

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-04-04

Naegi Makoto

5950X

357629800375982805907879

1132845877868291721291871011748754746231

A300ECC85181149E

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 = 385000, B2 = 9721250 (P-1 stage 2)

B1 = 385000 (P-1 stage 1)

B1 = 30000, B2 = 352500 (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