M2011957 Mersenne number exponent details

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M2011957

<<<

>>>

is 2 ^2011957 - 1

has 605660 decimal digits

takes 0.132 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	4EB6FBA02B5BC5F8	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	14.7687	68.6567%	580000	15080000	0.1306	5.2203%	14.8993	70.2929%	1.6362%
PrimeNet	2⁵⁸	0.0191	63.7931%	9000	150000	0.0016	2.6100%	0.0207	64.7381%	0.9450%
GPU72	2⁶²	0.3054	66.1290%	8000	120000	0.0013	1.2722%	0.3067	66.5600%	0.4309%
Difference	+5	+14.4633	+2.5277%	+572000	+14960000	+0.1293	+3.9480%	+14.5926	+3.7330%	+3.7330%

Known prime factors (1 factor, 71.3 bits, 0.00354597% 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
2011957	2995819168374884379599	22	71.343	744503776267307 7 × 251 × 618971 × 684581	2017-10-30	618971	684581	252.39	0.0594	0.1201

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.040%
2003-01-25T00:00:00	ANONYMOUS	v4_computers	30000	547500		-		-	-	0.006	-	-	1.425%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.273%
2010-12-02T22:33:00	Jocelyn Larouche	Manual testing	201195	201195		-		-	-	0.019	-	-	1.329%
2013-10-09T03:32:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	5.220%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-05T02:20:00	Sturle Sunde	corbusier.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-01-31T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.153	-	-
2013-02-11T20:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.488	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.976	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.857	-	-
2015-10-29T11:36:21	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.714	-	-
2016-07-16T16:15:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.428	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.602 GHz-days
Estimated T-Level:	3.900

Digits	B1	Curves	Complete	FacMiss
20	11000	78 / 100	0.780	45.661%
25	50000	78 / 280	0.279	75.649%

New Calculation Method

Total ECM effort:	6.602 GHz-days
Estimated T-Level:	3.900

Digits	B1	Complete	FacMiss
20	11000	3.000	4.979%
25	50000	0.278	75.761%
30	250000	0.018	98.264%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.793
50000	5000000	2995819168374884379599	45	3.809

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-28T23:25:00	Architects Cubed	m1_35	50000	5000000						3	0.254
2009-09-06T22:49:00	SubPrime	abd0	50000	5000000						3	0.254
2011-07-01T10:25:00	mm	ASW005	50000	5000000						3	0.254
2013-01-25T17:52:00	Sara	Sara	50000	5000000						3	0.254
2014-03-17T06:20:00	Bruce	snowflake	50000	5000000						3	0.254
2015-06-29T14:09:00	guru	w1	50000	5000000						3	0.254
2015-09-02T07:22:00	mikr	MSI	50000	5000000						12	1.016
2017-04-28T14:49:45	Bruce	Desk6	50000	5000000						3	0.254
2017-10-30T20:04:51	Sid & Andy	Woody	50000	5000000	2995819168374884379599	71.343	45	2		45	3.809

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	4EB6FBA02B5BC5F8	0.132
2016-06-21T11:38:33	Mark Rose	slink	4EB6FBA02B5BC5F8	0.132

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-31T13:00:21

YarBer

Manual testing

2995819168374884379599

060AB4439DF475__

2017-10-31T23:51:46

Oliver Kruse

GTX-3

2995819168374884379599

060AB4439DF475__

2017-11-01T06:53:19

YarBer

Manual testing

2995819168374884379599

060AB4439DF475__

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 = 580000, B2 = 15080000 (P-1 stage 2)

B1 = 580000 (P-1 stage 1)

B1 = 201195 (P-1 stage 1)

B1 = 30000, B2 = 547500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 3000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-11-01T06:53:19+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