M2596943 Mersenne number exponent details

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M2596943

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is 2 ^2596943 - 1

has 781758 decimal digits

takes 0.180 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	EFE75F4A19F2D3D4	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	11.4419	67.1642%	175000	4156250	0.0394	3.5535%	11.4813	68.3310%	1.1668%
PrimeNet	2⁵⁹	0.0296	62.7119%	11000	200000	0.0021	2.6943%	0.0317	63.7165%	1.0047%
GPU72	2⁶³	0.6146	65.0794%	12000	200000	0.0022	1.5300%	0.6168	65.6136%	0.5343%
Difference	+4	+10.8273	+2.0848%	+163000	+3956250	+0.0372	+2.0235%	+10.8645	+2.7174%	+2.7174%

Known prime factors (1 factor, 78.8 bits, 0.00303519% 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
2596943	534314306132636284453543	24	78.822	102873706918603197 3 × 34291235639534399	2015-10-03	3	34291235639534399	42,232	187,899,778	350,944,459

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	-	-	0.294%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.913%
2010-11-16T23:08:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.317%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.622%
2011-04-18T05:14:00	James Heinrich	WHS	175000	4156250		-		-	-	0.039	-	-	3.554%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11T04:28:46	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.059	-	-
2009-01-29T05:25:00	Sturle Sunde	nouchcraft.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-23T10:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.378	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.756	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.439	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.294 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:	1.294 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.538	58.365%
25	50000	0.050	95.140%
30	250000	0.003	99.686%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.110
50000	5000000	534314306132636284453543	2	0.185

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-28T23:55:00	Aca Arsov	backo6400	50000	5000000						3	0.277
2010-05-26T14:28:00	Lupo	yorick	50000	5000000						3	0.277
2012-11-14T06:53:00	Donna Noble	PH2x6	50000	5000000						3	0.277
2014-07-21T17:01:00	Kripke	Kripke	50000	5000000						3	0.277
2015-10-03T05:52:23	lopper	i5-4670	50000	5000000	534314306132636284453543	78.822	2	2		2	0.185

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-12T00:00:00	ANONYMOUS	v4_computers	EFE75F4A19F2D3D4	0.180
1999-04-23T00:00:00	ANONYMOUS	v4_computers	EFE75F4A19F2D3D4	0.180

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:59

alpertron

Manual testing

534314306132636284453543

28CD03DA9D42FB__

2017-11-12T15:16:59

Oliver Kruse

GTX-3

534314306132636284453543

28CD03DA9D42FB__

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 = 175000, B2 = 4156250 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (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)

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TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

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2¹⁰⁰

Last modified: 2022-03-11T04:28:46+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