M2151629 Mersenne number exponent details

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M2151629

<<<

>>>

is 2 ^2151629 - 1

has 647705 decimal digits

takes 0.141 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	51D5EDADAC4583DE	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	13.8100	67.1642%	2500000	125000000	0.8746	8.5862%	14.6846	69.9835%	2.8194%
PrimeNet	2⁵⁸	0.0178	62.0690%	9000	170000	0.0017	2.7341%	0.0195	63.1060%	1.0371%
GPU72	2⁶²	0.2855	64.5161%	10000	160000	0.0017	1.5180%	0.2873	65.0548%	0.5387%
Difference	+5	+13.5244	+2.6481%	+2490000	+124840000	+0.8729	+7.0682%	+14.3973	+4.9288%	+4.9288%

Known prime factors (1 factor, 91.3 bits, 0.00424206% 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
2151629	2992501240198175548946003479	28	91.273	695403631434177441591 3 × 19 × 1495867 × 1729727 × 4715107	2017-12-08	1729727	4715107	332,507,690	0.1804	0.3356

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2010-11-03T21:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.303%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.417%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.599%
2011-01-23T18:21:00	James Heinrich	i7-920	135000	2666250		-		-	-	0.026	-	-	3.006%
2016-05-02T01:23:02	Jocelyn Larouche	Manual testing	270000	9955453	12	-		-	-	0.076	-	-	4.414%
2017-10-04T07:45:20	Jocelyn Larouche	low 4M	540000	5400000	6	-		-	-	0.077	-	-	4.233%
2017-11-17T22:14:08	Jocelyn Larouche	low 4M	648000	10950998	12	-		-	-	0.115	-	-	5.005%
2017-12-08T23:13:31	mikr	MSI	2500000	125000000	12		2992501240198175548946003479	28	91.273	0.875	0.283	1.749	8.586%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T17:51:00	Sturle Sunde	rodolfo.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T20:00:00	Sturle Sunde	klughardt.ifi	2⁶¹	2⁶²		-	-	0.143	-	-
2013-09-08T17:50:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.456	-	-
2015-03-18T15:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.912	-	-
2015-03-18T15:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.737	-	-
2015-12-30T18:01:32	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.473	-	-
2016-11-04T03:09:02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.946	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.749 GHz-days
Estimated T-Level:	2.000

Digits	B1	Curves	Complete	FacMiss
20	11000	40 / 100	0.400	66.897%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	2.749 GHz-days
Estimated T-Level:	2.000

Digits	B1	Complete	FacMiss
20	11000	0.970	37.910%
25	50000	0.087	91.624%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
11000	1100000		10	0.188
50000	5000000		30	2.561

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-18T12:19:00	mognuts	hallowes	50000	5000000						3	0.256
2009-11-29T00:41:00	Piepen	T41-2000	50000	5000000						3	0.256
2011-08-15T01:42:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-25T18:20:00	Donna Noble	opt4820	50000	5000000						3	0.256
2013-08-24T12:53:00	Matthias Wurtinger	i5-750	11000	1100000						10	0.188
2015-07-13T16:59:00	guru	w6	50000	5000000						3	0.256
2016-02-20T09:57:38	Sintax	cloud	50000	5000000						3	0.256
2016-05-17T05:03:00	Bruce	Desk6	50000	5000000						3	0.256
2016-08-29T13:09:23	StarionHost	Bluto	50000	5000000						3	0.256
2017-01-24T16:18:53	Bruce	Desk6	50000	5000000						3	0.256
2017-08-22T19:44:49	Bruce	Desk6	50000	5000000						3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-26T00:00:00	ANONYMOUS	v4_computers	51D5EDADAC4583DE	0.141

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-09T07:46:32

YarBer

Manual testing

2992501240198175548946003479

9804C0E38DCC45__

2017-12-09T09:49:37

YarBer

Manual testing

2992501240198175548946003479

9804C0E38DCC45__

2017-12-12T04:51:46

trebor

Desktop

2992501240198175548946003479

9804C0E38DCC45__

2017-12-12T07:25:57

kkmrkkblmbrbk

c4.xlarge

2992501240198175548946003479

9804C0E38DCC45__

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 648000, B2 = 10950998 (P-1 stage 2)

B1 = 540000, B2 = 5400000 (P-1 stage 2)

B1 = 270000, B2 = 9955453 (P-1 stage 2)

B1 = 648000 (P-1 stage 1)

B1 = 540000 (P-1 stage 1)

B1 = 135000, B2 = 2666250 (P-1 stage 2)

B1 = 270000 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (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

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-12-12T07:25:57+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