M6 926 239 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	138.0740	68.0556%	4000000	414323910	8.3331	7.9720%	146.4071	70.6022%
Target	2⁶⁷	4.2901	65.6716%	45000	900000	0.0290	2.2366%	4.3190	66.4394%
Difference	+5	+133.7840	+2.3839%	+3955000	+413423910	+8.3042	+5.7354%	+142.0881	+4.1627%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-10-20	ANONYMOUS	v4_computers	35000	472500		-		-	-	0.019	-	-	0.884%
2012-08-16	Nesowa	EPC	85000	1508750		-		-	-	0.051	-	-	1.565%
2018-03-16	Squeeky_Squirrel	i5-5250U_1600	405000	12251250	12	-		-	-	0.332	-	-	3.405%
2021-06-02	Dylan Delgado	Manual testing	630000	18900000	12	-		-	-	0.514	-	-	3.947%
2021-11-27	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.531%
2021-12-02	Seth_Tr	Manual testing	4000000	414323910		-		-	-	8.333	-	-	7.972%

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	2⁶²		-	-	0.089	-	-
1999-10-15	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-17	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.539	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.079	-	-
2016-04-03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.158	-	-
2018-05-23	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.316	-	-
2020-05-01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.631	-	-
2021-07-22	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.26	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.52	-	-
2021-10-11	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.05	-	-

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
2012-08-17	Arne Kleppestrand	Arne	50000	5000000						3	0.995
2017-04-03	Bruce	Desk8	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15	ANONYMOUS	v4_computers	C6097014F7AA19__	1.510
2000-07-12	ANONYMOUS	v4_computers	C86EB89525327607	1.510
2001-12-22	ANONYMOUS	v4_computers	C86EB89525327607	1.510

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 = 414323910 (P-1 stage 2)

B1 = 4000000, B2 = 110000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 630000, B2 = 18900000 (P-1 stage 2)

B1 = 405000, B2 = 12251250 (P-1 stage 2)

B1 = 630000 (P-1 stage 1)

B1 = 405000 (P-1 stage 1)

B1 = 85000, B2 = 1508750 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 35000, B2 = 472500 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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