M2543249 Mersenne number exponent details

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M2543249

<<<

>>>

is 2 ^2543249 - 1

has 765595 decimal digits

takes 0.176 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	CACCCD5517D7F2FB	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	2⁶⁸	23.4365	67.6471%	3000000	135000000	1.0250	8.2626%	24.4615	70.3202%	2.6732%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6839%	0.0323	63.7127%	1.0008%
GPU72	2⁶³	0.6276	65.0794%	12000	180000	0.0021	1.4772%	0.6297	65.5952%	0.5159%
Difference	+5	+22.8090	+2.5677%	+2988000	+134820000	+1.0229	+6.7853%	+23.8318	+4.7250%	+4.7250%

Known prime factors (1 factor, 73.5 bits, 0.00288984% 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
2543249	13317260328390416115943	23	73.496	2618158962883779 3⁴ × 7 × 4617564308437	2020-07-01	81	4617564308437	953.85	25,302	47,257

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	-	-	0.236%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.755%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.265%
2011-01-03T01:02:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.366%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.531%
2011-02-28T16:45:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	3.959%
2018-08-13T10:35:02	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.048%
2018-09-19T11:40:17	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	8.263%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
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	-	-
2009-01-31T15:27:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T13:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.386	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.772	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.469	-	-
2015-11-08T21:03:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.938	-	-
2017-08-08T13:42:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.877	-	-
2019-04-08T13:40:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.779 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.779 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.323	26.645%
25	50000	0.120	88.733%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.595
50000	5000000	13317260328390416115943	2	0.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-01T10:57:00	ksims	ZhViZCJBj2sims	50000	5000000						3	0.277
2010-04-30T08:51:00	SubPrime	abd0	50000	5000000						3	0.277
2012-09-27T00:36:00	Bud	annan	50000	5000000						3	0.277
2014-03-29T22:49:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-07T05:25:00	guru	w6	50000	5000000						3	0.277
2016-03-11T13:10:19	Marius Zens	KBWR_TV3	50000	5000000						3	0.277
2016-07-17T20:10:06	lettp	Home	50000	5000000						3	0.277
2017-05-19T11:07:10	Ensigma	vps_sing	50000	5000000						3	0.277
2017-09-28T07:10:29	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2018-02-22T00:20:10	MaFa	free_gce	50000	5000000						3	0.277
2018-11-13T13:31:53	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2020-06-17T10:37:41	mnd9	touchdown	50000	5000000						3	0.277
2020-06-22T18:52:12	LaurV	3tits	50000	5000000						3	0.277
2020-07-01T18:54:09	daveward2005	Davy	50000	5000000	13317260328390416115943	73.496	2	2		2	0.184

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	CACCCD5517D7F2FB	0.176
2018-06-10T10:37:18	kkmrkkblmbrbk	old	CACCCD5517D7F2FB	0.176

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-02T12:45:25

mrh.org

13317260328390416115943

D9DD30CCA8C23FE5

2020-07-03T09:46:41

marssystems

system03

13317260328390416115943

D9DD30CCA8C23FE5

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 = 30000 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-03T09:46:41+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