M2549423 Mersenne number exponent details

≡

M2549423

<<<

>>>

is 2 ^2549423 - 1

has 767453 decimal digits

takes 0.177 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	AC3D940E7B102391	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	11.6552	67.1642%	3000000	135000000	1.0250	8.9485%	12.6802	70.1025%	2.9383%
PrimeNet	2⁵⁹	0.0301	62.7119%	11000	200000	0.0021	2.6851%	0.0323	63.7131%	1.0012%
GPU72	2⁶³	0.6260	65.0794%	12000	180000	0.0021	1.4780%	0.6282	65.5955%	0.5161%
Difference	+4	+11.0291	+2.0848%	+2988000	+134820000	+1.0229	+7.4705%	+12.0520	+4.5070%	+4.5070%

Known prime factors (1 factor, 86.7 bits, 0.00340183% 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
2549423	128065990677199185591698089	27	86.727	25116661824498952428 2² × 3 × 7² × 71 × 503 × 20593 × 58081609	2018-10-22	20593	58081609	10,282,365	0.3202	0.5944

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.292%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.884%
2010-12-19T21:43:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.315%
2011-01-08T14:34:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-02-24T21:59:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	4.387%
2018-08-17T10:20:10	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.470%
2018-10-22T17:45:12	mikr	MSI	3000000	135000000	12		128065990677199185591698089	27	86.727	1.025	0.354	2.050	8.948%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.015	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-28T21:35:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-16T06:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.385	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.770	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.466	-	-
2015-11-08T21:02:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.931	-	-
2017-08-08T13:42:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.862	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.766 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	2.766 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	0.968	37.994%
25	50000	0.087	91.625%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.766

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-17T02:39:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.277
2010-05-03T17:12:00	Lupo	yorick	50000	5000000						3	0.277
2012-10-04T07:26:00	Bud	annan	50000	5000000						3	0.277
2014-04-06T14:23:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-09T03:19:00	guru	w6	50000	5000000						3	0.277
2016-03-08T03:01:59	Jason U	Server7	50000	5000000						3	0.277
2016-07-19T17:41:52	lettp	Home	50000	5000000						3	0.277
2017-05-20T12:29:06	Bruce	eleven	50000	5000000						3	0.277
2017-10-02T06:50:37	Sebastian Hornbostel	V2	50000	5000000						3	0.277
2018-03-02T23:31:06	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-13T00:00:00	ANONYMOUS	v4_computers	AC3D940E7B102391	0.177
1999-03-26T00:00:00	ANONYMOUS	v4_computers	AC3D940E7B102391	0.177
2018-06-11T20:46:13	kkmrkkblmbrbk	old	AC3D940E7B102391	0.177

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-10-24T18:13:45

marcomich

sisg6

128065990677199185591698089

21E64952042EB8__

2018-10-24T18:38:34

ATH

ec2-PRPCFDC

128065990677199185591698089

21E64952042EB8__

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 = 3000000, B2 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (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

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-10-24T18:38:34+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