M2765473 Mersenne number exponent details

Residue

Status

L-L

41B0EA664B8926E4

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	10.7446	67.1642%	2700000	84000000	0.7984	8.3336%	11.5430	69.9006%	2.7364%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8554%	0.0304	63.7766%	1.0647%
GPU72	2⁶³	0.5771	65.0794%	15000	240000	0.0031	1.7457%	0.5802	65.6890%	0.6096%
Difference	+4	+10.1675	+2.0848%	+2685000	+83760000	+0.7954	+6.5879%	+10.9629	+4.2116%	+4.2116%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.7446

67.1642%

2700000

84000000

0.7984

8.3336%

11.5430

69.9006%

2.7364%

PrimeNet

2⁵⁹

0.0278

62.7119%

12000

220000

0.0026

2.8554%

0.0304

63.7766%

1.0647%

GPU72

2⁶³

0.5771

65.0794%

15000

240000

0.0031

1.7457%

0.5802

65.6890%

0.6096%

Difference

+10.1675

+2.0848%

+2685000

+83760000

+0.7954

+6.5879%

+10.9629

+4.2116%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2765473	991025794184657973729908561	27	89.679	179178352886587208360 2³ × 5 × 313 × 19463 × 151343 × 4858577	2017-01-29	151343	4858577	79,090,332	0.0457	0.0554

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2765473

991025794184657973729908561

89.679

179178352886587208360
2³ × 5 × 313 × 19463 × 151343 × 4858577

2017-01-29

151343

4858577

79,090,332

0.0457

0.0554

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.299%
2010-12-02T05:12:00	markr	tiny	110000	2365000		-		-	-	0.026	-	-	2.927%
2016-08-11T02:58:16	Jocelyn Larouche	Manual testing	142000	4730000	6	-		-	-	0.044	-	-	3.559%
2016-10-27T01:50:42	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.289%
2016-12-24T02:28:25	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.413%
2017-01-29T20:16:51	mikr	MSI	2700000	84000000	12		991025794184657973729908561	27	89.679	0.798	0.427	1.597	8.334%
2017-02-25T21:08:01	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.562%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.056	-	-
2009-01-31T05:29:00	Sturle Sunde	gofy.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-14T05:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.355	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.710	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.351	-	-
2016-02-08T11:13:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.702	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.183 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	2.183 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	2.183

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-17T09:31:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.312
2010-09-17T19:28:00	James Hintz	ryan	50000	5000000						3	0.312
2013-03-05T21:00:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-13T03:23:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T15:26:29	Sintax	cloud2	50000	5000000						3	0.312
2016-05-18T03:10:51	lettp	Home	50000	5000000						3	0.312
2017-01-17T01:47:28	Bruce	eleven	50000	5000000						3	0.312

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	41B0EA664B8926E4	0.214

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

41B0EA664B8926E4

0.214

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20T21:58:18

Oliver Kruse

GTX-2

991025794184657973729908561

9CDFF8272E848E__

2017-12-06T00:26:54

kkmrkkblmbrbk

c4.xlarge

991025794184657973729908561

9CDFF8272E848E__

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 294451, B2 = 2944510 (P-1 stage 2)

B1 = 142000, B2 = 4730000 (P-1 stage 2)

B1 = 294451 (P-1 stage 1)

B1 = 110000, B2 = 2365000 (P-1 stage 2)

B1 = 204480 (P-1 stage 1)

B1 = 170400 (P-1 stage 1)

B1 = 142000 (P-1 stage 1)

B1 = 110000 (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

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