M6 928 661 Mersenne number exponent details

Residue

Status

L-L

289B04428AFC90CE

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	138.0258	68.0556%	2000000	258849360	5.0569	6.9787%	143.0827	70.2849%
Target	2⁶⁷	4.2886	65.6716%	45000	900000	0.0290	2.2367%	4.3175	66.4395%
Difference	+5	+133.7372	+2.3839%	+1955000	+257949360	+5.0280	+4.7420%	+138.7652	+3.8454%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

138.0258

68.0556%

2000000

258849360

5.0569

6.9787%

143.0827

70.2849%

Target

2⁶⁷

4.2886

65.6716%

45000

900000

0.0290

2.2367%

4.3175

66.4395%

Difference

+133.7372

+2.3839%

+1955000

+257949360

+5.0280

+4.7420%

+138.7652

+3.8454%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-31	ANONYMOUS	v4_computers	30000	30000		-		-	-	0.009	-	-	0.234%
2011-09-04	Carsten Kossendey	mother	440000	13310000		-		-	-	0.361	-	-	3.505%
2021-06-02	Dylan Delgado	Manual testing	630000	18900000	12	-		-	-	0.514	-	-	3.947%
2021-12-07	Seth_Tr	Manual testing	2000000	258849360		-		-	-	5.057	-	-	6.979%

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	2⁶¹		-	-	0.044	-	-
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
1998-08-02	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-02-18	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		-	-	2.157	-	-
2018-02-25	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.314	-	-
2020-05-01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.628	-	-
2021-07-22	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.26	-	-
2021-08-10	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.51	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.03	-	-

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
2012-08-21	Brett Walker		50000	5000000						3	0.995
2017-04-05	Bruce	Desk7	50000	5000000						3	0.995

date	userid	compid	res64	spent (GHz-days)
2000-01-04	ANONYMOUS	v4_computers	289B04428AFC90CE	1.511
2001-11-10	ANONYMOUS	v4_computers	289B04428AFC90CE	1.511

date

userid

compid

res64

spent (GHz-days)

2000-01-04

ANONYMOUS

v4_computers

289B04428AFC90CE

1.511

2001-11-10

ANONYMOUS

v4_computers

289B04428AFC90CE

1.511

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 = 2000000, B2 = 258849360 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

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

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

B1 = 630000 (P-1 stage 1)

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

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.7

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