M2210581 Mersenne number exponent details

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M2210581

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>>>

is 2 ^2210581 - 1

has 665452 decimal digits

takes 0.145 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	478A40829FF74A63	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	13.4417	67.1642%	2000000	65000000	0.5179	7.6495%	13.9596	69.6760%	2.5118%
PrimeNet	2⁵⁸	0.0174	62.0690%	10000	180000	0.0018	2.8656%	0.0192	63.1559%	1.0870%
GPU72	2⁶²	0.2779	64.5161%	11000	170000	0.0019	1.6016%	0.2798	65.0844%	0.5683%
Difference	+5	+13.1638	+2.6481%	+1989000	+64830000	+0.5160	+6.0480%	+13.6798	+4.5915%	+4.5915%

Known prime factors (1 factor, 73.6 bits, 0.00333074% 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
2210581	14602223625623700746593	23	73.629	3302802210284016 2⁴ × 3 × 11 × 29 × 215700248843	2017-05-03	29	215700248843	1,063.1	1,120.4	2,092.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.281%
2010-11-06T00:22:00	ANONYMOUS	Manual testing	15000	15000		-		-	-	0.001	-	-	0.239%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.419%
2011-01-08T14:42:00	markr	tiny	90000	1665000		-		-	-	0.017	-	-	2.510%
2014-06-24T22:45:00	Jocelyn Larouche	Manual testing	119035	119035		-		-	-	0.011	-	-	1.023%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	148070	148070		-		-	-	0.014	-	-	1.152%
2015-11-12T05:08:10	Alexander Dubrovin	Manual testing	600000	2500000	6	-		-	-	0.067	-	-	3.550%
2015-11-12T05:08:11	Alexander Dubrovin	Manual testing	1200000	5500000	6	-		-	-	0.137	-	-	4.541%
2015-11-13T05:07:50	Alexander Dubrovin	Manual testing	1600000	8500000	12	-		-	-	0.188	-	-	5.113%
2015-11-13T05:07:51	Alexander Dubrovin	Manual testing	1800000	11000000	12	-		-	-	0.219	-	-	5.452%
2015-11-13T19:53:09	Alexander Dubrovin	Manual testing	1800000	35000000	12	-		-	-	0.344	-	-	6.836%
2015-12-10T16:59:14	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.650%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-02T23:05:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2009-01-08T05:07:00	Sturle Sunde	bruckner.ifi	2⁶¹	2⁶²		-	-	0.139	-	-
2013-12-04T10:24:00	LaurV	Manual testing	2⁶²	2⁶³		-	-	0.444	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.888	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.690	-	-
2015-10-22T10:17:21	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.380	-	-
2016-12-12T15:11:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.761	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.484 GHz-days
Estimated T-Level:	1.450

Digits	B1	Curves	Complete	FacMiss
20	11000	29 / 100	0.290	74.717%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	2.484 GHz-days
Estimated T-Level:	1.450

Digits	B1	Complete	FacMiss
20	11000	0.935	39.240%
25	50000	0.085	91.893%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.313
50000	5000000	14602223625623700746593	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-07T22:51:00	dragon325	x-liberty	50000	5000000						3	0.257
2009-12-16T16:04:00	KAMCOBILL	PC01	50000	5000000						3	0.257
2011-09-15T13:30:00	S36049	Wolle5	50000	5000000						3	0.257
2013-06-08T16:48:00	hiems	Laptop	50000	5000000						3	0.257
2015-03-15T03:15:00	Jason U	Server7	50000	5000000						3	0.257
2016-03-18T11:49:56	S36049	Wolle5	50000	5000000						3	0.257
2016-03-27T23:09:38	Bruce	Desk6	50000	5000000						3	0.257
2016-07-03T03:51:21	Bruce	Desk6	50000	5000000						3	0.257
2016-11-17T09:47:18	NBCC		50000	5000000						3	0.257
2017-05-03T10:22:39	Bruce	Desk6	50000	5000000	14602223625623700746593	73.629	2	2		2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	cmorton	v4_computers	478A40829FF74A63	0.145

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:08:42

alpertron

Manual testing

14602223625623700746593

B0C59A8676BC66__

2017-10-25T22:53:35

Oliver Kruse

GTX-2

14602223625623700746593

B0C59A8676BC66__

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 = 2000000, B2 = 65000000 (P-1 stage 2)

B1 = 1800000, B2 = 35000000 (P-1 stage 2)

B1 = 1800000, B2 = 11000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1600000, B2 = 8500000 (P-1 stage 2)

B1 = 1800000 (P-1 stage 1)

B1 = 1600000 (P-1 stage 1)

B1 = 1200000, B2 = 5500000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 600000, B2 = 2500000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 90000, B2 = 1665000 (P-1 stage 2)

B1 = 148070 (P-1 stage 1)

B1 = 119035 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-10-25T22:53:35+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