M6 940 561 Mersenne number exponent details

Residue

Status

L-L

9CA9DFF8D968B55E

double-checked

PRP

FE7E3EB221C1A1D0

PRP-tested

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.7891	68.0556%	4000000	456818670	9.0652	8.0804%	146.8543	70.6368%
Target	2⁶⁷	4.2812	65.6716%	45000	900000	0.0290	2.2374%	4.3102	66.4397%
Difference	+5	+133.5079	+2.3839%	+3955000	+455918670	+9.0362	+5.8430%	+142.5441	+4.1971%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷²

137.7891

68.0556%

4000000

456818670

9.0652

8.0804%

146.8543

70.6368%

Target

2⁶⁷

4.2812

65.6716%

45000

900000

0.0290

2.2374%

4.3102

66.4397%

Difference

+133.5079

+2.3839%

+3955000

+455918670

+9.0362

+5.8430%

+142.5441

+4.1971%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6940561	6038598188823193205446529	25	82.320	435022341048741824 2⁶ × 7 × 293 × 12743 × 260072387	2021-12-02	12743	260072387	147,964	4.4839	8.3676

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6940561

6038598188823193205446529

82.320

435022341048741824
2⁶ × 7 × 293 × 12743 × 260072387

2021-12-02

12743

260072387

147,964

4.4839

8.3676

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	30000	30000		-		-	-	0.009	-	-	0.234%
2011-09-05	Carsten Kossendey	mother	440000	13310000		-		-	-	0.361	-	-	3.506%
2021-11-17	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.983%
2021-12-02	Seth_Tr	Manual testing	4000000	456818670			6038598188823193205446529	25	82.320	9.065	3.027	18.13	8.080%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1999-01-02	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2004-10-18	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.283	-	-
2014-02-16	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.538	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.077	-	-
2016-04-05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.153	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.307	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.613	-	-
2021-07-28	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.23	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.45	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.91	-	-

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
2012-08-27	MadPoo	IntLAVH03	50000	5000000						3	0.995
2017-04-11	ANONYMOUS		50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	Ken Warner	v4_computers	B168A46CADAC6A__	1.513
1999-06-15	ANONYMOUS	v4_computers	9CA9DFF8D968B55E	1.513
2000-03-22	Ken Warner	v4_computers	B168A46CADAC6A__	1.513
2002-01-02	ANONYMOUS	v4_computers	9CA9DFF8D968B55E	1.513
2002-03-03	ANONYMOUS	v4_computers	9CA9DFF8D968B55E	1.513

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 = 456818670 (P-1 stage 2)

B1 = 3000000, B2 = 75000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3000000 (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

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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