M6 909 949 Mersenne number exponent details

Residue

Status

L-L

59187776CD346130

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	138.3995	68.0556%	4000000	110000000	3.0907	6.5297%	141.4902	70.1414%
Target	2⁶⁷	4.3002	65.6716%	45000	900000	0.0290	2.2357%	4.3291	66.4391%
Difference	+5	+134.0994	+2.3839%	+3955000	+109100000	+3.0618	+4.2940%	+137.1611	+3.7023%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

138.3995

68.0556%

4000000

110000000

3.0907

6.5297%

141.4902

70.1414%

Target

2⁶⁷

4.3002

65.6716%

45000

900000

0.0290

2.2357%

4.3291

66.4391%

Difference

+134.0994

+2.3839%

+3955000

+109100000

+3.0618

+4.2940%

+137.1611

+3.7023%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-24	Pi_Rho	v4_computers	30000	30000		-		-	-	0.009	-	-	0.234%
2011-09-03	Carsten Kossendey	mother	440000	13310000		-		-	-	0.361	-	-	3.504%
2021-11-22	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.530%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-29	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-08-16	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2004-07-26	Sturle Sunde	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-18	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.541	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.081	-	-
2016-04-01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.163	-	-
2018-02-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.326	-	-
2019-12-13	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	8.652	-	-
2020-12-23	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.30	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.61	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.21	-	-

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
2012-08-13	JimBa	Dell	50000	5000000						3	0.995
2017-03-28	Bruce	Desk7	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23	curtisc	v4_computers	59187776CD346130	1.507
2001-10-20	Pi_Rho	v4_computers	59187776CD346130	1.507

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 = 110000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 440000, B2 = 13310000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 30000 (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