M2627291 Mersenne number exponent details

Residue

Status

L-L

1661F6374C07463F

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	11.3097	67.1642%	2000000	60000000	0.5779	7.6862%	11.8876	69.6880%	2.5238%
PrimeNet	2⁵⁹	0.0292	62.7119%	11000	200000	0.0024	2.7001%	0.0316	63.7187%	1.0068%
GPU72	2⁶³	0.6075	65.0794%	13000	200000	0.0026	1.5721%	0.6101	65.6284%	0.5490%
Difference	+4	+10.7022	+2.0848%	+1987000	+59800000	+0.5753	+6.1141%	+11.2775	+4.0596%	+4.0596%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.3097

67.1642%

2000000

60000000

0.5779

7.6862%

11.8876

69.6880%

2.5238%

PrimeNet

2⁵⁹

0.0292

62.7119%

11000

200000

0.0024

2.7001%

0.0316

63.7187%

1.0068%

GPU72

2⁶³

0.6075

65.0794%

13000

200000

0.0026

1.5721%

0.6101

65.6284%

0.5490%

Difference

+10.7022

+2.0848%

+1987000

+59800000

+0.5753

+6.1141%

+11.2775

+4.0596%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2627291	188560915422777827921	21	67.354	35885045741560 2³ × 5 × 1933 × 464110783	2015-12-13	1933	464110783	12.295	2.8320	5.2891

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2627291

188560915422777827921

67.354

35885045741560
2³ × 5 × 1933 × 464110783

2015-12-13

1933

464110783

12.295

2.8320

5.2891

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.295%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.915%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.318%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.435%
2011-01-19T23:50:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.623%
2011-02-27T16:00:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	4.404%
2019-07-04T12:42:51	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.578	-	-	7.686%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	Ethan O'Connor	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2022-03-11T04:28:50	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.058	-	-
2009-02-13T04:37:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-06-12T03:57:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.117	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.374	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.747	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.422	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.444 GHz-days
Estimated T-Level:	0.700

Digits	B1	Curves	Complete	FacMiss
20	11000	14 / 100	0.140	86.875%
25	50000	14 / 280	0.050	95.114%

New Calculation Method

Total ECM effort:	1.444 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.452	63.660%
25	50000	0.041	96.001%
30	250000	0.003	99.749%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.238
50000	5000000	188560915422777827921	2	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-04T17:05:00	Aca Arsov	backo6400	50000	5000000						3	0.309
2010-06-15T20:59:00	James Classen	towerofart	50000	5000000						3	0.309
2012-11-25T03:38:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.309
2014-10-02T04:15:00	arnaud	srv-630	50000	5000000						3	0.309
2015-12-13T12:32:35	guru	w1	50000	5000000	188560915422777827921	67.354	2	2		2	0.206

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	Ethan O'Connor	v4_computers	1661F6374C07463F	0.203

date

userid

compid

res64

spent (GHz-days)

1999-04-13T00:00:00

Ethan O'Connor

v4_computers

1661F6374C07463F

0.203

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:30:57

alpertron

Manual testing

188560915422777827921

8639D5CF03310D__

2017-11-13T22:02:42

Oliver Kruse

GTX-1

188560915422777827921

8639D5CF03310D__

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 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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