M2757617 Mersenne number exponent details

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M2757617

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>>>

is 2 ^2757617 - 1

has 830126 decimal digits

takes 0.213 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	443A9FCE8B25FC7E	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	10.7752	67.1642%	2700000	84000000	0.7984	8.3313%	11.5737	69.8998%	2.7356%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8539%	0.0305	63.7760%	1.0642%
GPU72	2⁶³	0.5788	65.0794%	15000	240000	0.0031	1.7448%	0.5818	65.6886%	0.6093%
Difference	+4	+10.1964	+2.0848%	+2685000	+83760000	+0.7954	+6.5865%	+10.9918	+4.2112%	+4.2112%

Known prime factors (1 factor, 92.6 bits, 0.00335784% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2757617	7487051004891945470527943089	28	92.596	1357521912015327993432 2³ × 3 × 17 × 41 × 10463 × 307939 × 25187317	2016-12-30	307939	25187317	657,512,940	0.1863	0.2870

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%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.934%
2010-12-21T11:04:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.321%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.440%
2011-01-23T12:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.630%
2011-05-08T16:25:00	James Heinrich	WHS	190000	4655000		-		-	-	0.049	-	-	3.717%
2016-12-30T13:42:00	mikr	MSI	2700000	84000000	12		7487051004891945470527943089	28	92.596	0.798	0.426	1.597	8.331%
2017-01-10T10:25:14	Jocelyn Larouche	low 4M	228000	228000		-		-	-	0.026	-	-	1.490%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:20	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.056	-	-
2009-02-14T04:13:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-26T08:20:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-10T10:19:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.356	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.712	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.355	-	-
2016-02-05T15:45:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.710	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.871 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.871 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.871

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-15T09:14:00	deekayen	classic-sharedtest	50000	5000000						3	0.312
2010-09-26T02:40:00	Anu Järvi	Anu-TEMP	50000	5000000						3	0.312
2013-03-02T20:36:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-10T19:44:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T06:51:14	Bruce	Desk8	50000	5000000						3	0.312
2016-05-15T14:34:11	Jason U	Server7	50000	5000000						3	0.312

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	443A9FCE8B25FC7E	0.213
1999-08-07T00:00:00	ANONYMOUS	v4_computers	443A9FCE8B25FC7E	0.213

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20T18:27:16

Oliver Kruse

GTX-1

7487051004891945470527943089

13E4EC38A0C917__

2017-12-05T20:47:44

kkmrkkblmbrbk

c4.xlarge

7487051004891945470527943089

13E4EC38A0C917__

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 = 190000, B2 = 4655000 (P-1 stage 2)

B1 = 228000 (P-1 stage 1)

B1 = 190000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-12-05T20:47:44+00:00

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