M2576257 Mersenne number exponent details

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M2576257

<<<

>>>

is 2 ^2576257 - 1

has 775531 decimal digits

takes 0.179 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	01389699C294C787	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	11.5338	67.1642%	3200000	112000000	0.9180	8.7525%	12.4518	70.0381%	2.8739%
PrimeNet	2⁵⁹	0.0298	62.7119%	11000	200000	0.0021	2.6903%	0.0320	63.7150%	1.0032%
GPU72	2⁶³	0.6195	65.0794%	12000	190000	0.0022	1.5049%	0.6217	65.6049%	0.5255%
Difference	+4	+10.9142	+2.0848%	+3188000	+111810000	+0.9158	+7.2476%	+11.8301	+4.4333%	+4.4333%

Known prime factors (2 factors, 178.2 bits, 0.00691719% 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
2576257	177970813031017488463	21	67.270	34540578255783 3 × 19 × 673 × 900408703	2022-02-22	673	900408703	20.582	4.9339	9.2150
2576257	2480649151812913240959229787439937	34	110.934	481444427285964335266091424 2⁵ × 3² × 7 × 23 × 43 × 1303 × 48221 × 478901 × 8024777	2016-07-03	478901	8024777	6.614e+10	0.0895	0.0980

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
2576257	177970813031017488463 2480649151812913240959229787439937	44148314639284809983908679711037562554406518820294 6831	54	178.205

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	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	202500		-		-	-	0.003	-	-	0.891%
2010-12-21T11:04:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-11T22:55:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.621%
2011-10-08T00:45:00	markr	tiny	175000	4112500		-		-	-	0.039	-	-	3.542%
2016-07-03T10:32:34	mikr	MSI	3200000	112000000	12		2480649151812913240959229787439937	34	110.934	0.918	0.357	1.836	8.752%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	Dry Creek Photo	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-02-01T12:15:00	Sturle Sunde	haydn.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-19T16:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.119	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.381	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.762	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.450	-	-
2015-11-08T21:03:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.901	-	-
2022-03-11T02:05:02	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	5.801	-	-
2022-02-22T10:09:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	177970813031017488463	67.270	21	9.048	0.363	18.39

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.662 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:	1.662 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	1.662

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-18T10:42:00	borkencode	CFF2DC1CD	50000	5000000						3	0.277
2010-05-14T20:12:00	James Classen	towerofart	50000	5000000						3	0.277
2012-10-21T06:55:00	Donna Noble	i3-2100t	50000	5000000						3	0.277
2014-06-30T13:15:00	Bruce	xps630	50000	5000000						3	0.277
2014-09-10T22:38:00	arnaud	srv-630	50000	5000000						3	0.277
2016-03-16T10:20:22	Dave Matthews	VMW7-001	50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	Dry Creek Photo	v4_computers	01389699C294C787	0.179

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T08:01:40

Oliver Kruse

GTX-2

2480649151812913240959229787439937

5101DE402A10E8__

2017-12-02T00:11:30

kkmrkkblmbrbk

c4.xlarge

2480649151812913240959229787439937

5101DE402A10E8__

2022-02-22T21:01:57

LordJulius

WhiteBox

177970813031017488463

2480649151812913240959229787439937

5101DE402A10E82F

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 = 3200000 (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 = 202500 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

Last modified: 2022-03-11T02:05:02+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