M2588753 Mersenne number exponent details

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M2588753

<<<

>>>

is 2 ^2588753 - 1

has 779293 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	D44424DAE0FD7423	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	11.4781	67.1642%	3200000	112000000	0.9180	8.7565%	12.3961	70.0395%	2.8753%
PrimeNet	2⁵⁹	0.0297	62.7119%	11000	200000	0.0021	2.6927%	0.0318	63.7159%	1.0041%
GPU72	2⁶³	0.6165	65.0794%	12000	200000	0.0022	1.5290%	0.6188	65.6133%	0.5339%
Difference	+4	+10.8616	+2.0848%	+3188000	+111800000	+0.9158	+7.2275%	+11.7773	+4.4261%	+4.4261%

Known prime factors (1 factor, 104.3 bits, 0.00402984% 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
2588753	25365396487879471541137460826049	32	104.323	4899153470392785936151008 2⁵ × 3² × 7 × 211 × 63247 × 3146371 × 57875959	2016-08-12	3146371	57875959	6.176e+10	0.6163	0.6440

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	206250		-		-	-	0.003	-	-	0.897%
2010-11-15T22:51:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-13T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.622%
2011-10-14T12:39:00	markr	tiny	175000	4112500		-		-	-	0.039	-	-	3.544%
2016-08-12T05:52:16	mikr	MSI	3200000	112000000	12		25365396487879471541137460826049	32	104.323	0.918	0.359	1.836	8.757%
2019-07-04T12:41:52	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.675%

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	-	-
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T00:40:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-22T17:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.119	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.379	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.758	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.443	-	-
2015-11-06T09:16:15	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.887	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.941 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:	1.941 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	1.941

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-23T03:51:00	Aca Arsov	backo6400	50000	5000000						3	0.277
2010-05-21T04:41:00	James Hintz	ryan	50000	5000000						3	0.277
2012-11-07T08:14:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.277
2014-06-23T13:56:00	Lukasz Wrobel	i-1	50000	5000000						3	0.277
2015-09-13T15:03:00	dragon325	Falken-i7-920	50000	5000000						3	0.277
2016-03-19T14:53:52	Dave Matthews	VMW7-001	50000	5000000						3	0.277
2016-08-07T16:24:14	lettp	Home	50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	D44424DAE0FD7423	0.180
1999-04-13T00:00:00	ANONYMOUS	v4_computers	D44424DAE0FD7423	0.180

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T12:26:59

Oliver Kruse

GTX-1

25365396487879471541137460826049

811A8450A24CF7__

2017-12-02T02:59:43

storm5510

HP-Z220-CMT

25365396487879471541137460826049

811A8450A24CF7__

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 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 175000, B2 = 4112500 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2019-07-04T12:41:52+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