M2719043 Mersenne number exponent details

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M2719043

<<<

>>>

is 2 ^2719043 - 1

has 818514 decimal digits

takes 0.210 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	4D3E77055A9DD687	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	10.9281	67.1642%	2700000	84000000	0.7984	8.3197%	11.7265	69.8960%	2.7319%
PrimeNet	2⁵⁹	0.0282	62.7119%	12000	220000	0.0026	2.8466%	0.0309	63.7733%	1.0615%
GPU72	2⁶³	0.5870	65.0794%	14000	220000	0.0028	1.6635%	0.5898	65.6603%	0.5809%
Difference	+4	+10.3411	+2.0848%	+2686000	+83780000	+0.7956	+6.6562%	+11.1367	+4.2357%	+4.2357%

Known prime factors (1 factor, 100.2 bits, 0.00368468% 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
2719043	1444157054376197466689696744129	31	100.188	265563482147247665206048 2⁵ × 31 × 1877 × 157259 × 200323 × 4527371	2016-10-05	200323	4527371	6.606e+10	0.0488	0.0516

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.298%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.922%
2010-12-19T21:41:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.320%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.439%
2011-01-18T22:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.628%
2011-04-24T14:14:00	James Heinrich	WHS	185000	4578750		-		-	-	0.048	-	-	3.682%
2016-10-05T05:18:43	mikr	MSI	2700000	84000000	12		1444157054376197466689696744129	31	100.188	0.798	0.420	1.597	8.320%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.056	-	-
2009-01-29T04:02:00	Sturle Sunde	ghirardelli.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-20T06:31:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.361	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.722	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.374	-	-
2016-01-31T12:58:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.748	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.866 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:	1.866 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	1.866

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-12T06:53:00	James Hintz	02_060209	50000	5000000						3	0.311
2010-08-22T02:13:00	Kamil_Górski	thefault	50000	5000000						3	0.311
2013-02-04T10:58:00	S00030	mac399	50000	5000000						3	0.311
2015-02-21T15:53:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-06T07:41:42	Jason U	Server7	50000	5000000						3	0.311
2016-05-03T18:21:04	lettp	Home	50000	5000000						3	0.311

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-08-16T00:00:00	ANONYMOUS	v4_computers	4D3E77055A9DD687	0.210
1999-05-02T00:00:00	ANONYMOUS	v4_computers	4D3E77055A9DD687	0.210

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-19T21:31:09

Oliver Kruse

GTX-0

1444157054376197466689696744129

2E1A1226BBD2C1__

2017-12-05T01:27:03

kkmrkkblmbrbk

c4.xlarge

1444157054376197466689696744129

2E1A1226BBD2C1__

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 185000, B2 = 4578750 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2017-12-05T01:27:03+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