M2158697 Mersenne number exponent details

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M2158697

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is 2 ^2158697 - 1

has 649833 decimal digits

takes 0.142 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	CD4210697129AA2A	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	13.7647	67.1642%	500000	15000000	0.1230	5.1703%	13.8877	68.8619%	1.6977%
PrimeNet	2⁵⁸	0.0178	62.0690%	10000	170000	0.0018	2.8099%	0.0196	63.1348%	1.0658%
GPU72	2⁶²	0.2846	64.5161%	10000	160000	0.0017	1.5191%	0.2863	65.0551%	0.5390%
Difference	+5	+13.4801	+2.6481%	+490000	+14840000	+0.1213	+3.6512%	+13.6014	+3.8067%	+3.8067%

Known prime factors (1 factor, 70.9 bits, 0.00328413% 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
2158697	2194433765487885130303	22	70.894	508277392678983 3 × 743 × 228029337227	2015-09-18	743	228029337227	123.71	1,184.4	2,212.2

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%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.237%
2010-11-07T01:16:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.417%
2010-11-07T12:40:00	Jocelyn Larouche	Manual testing	45000	45000		-		-	-	0.004	-	-	0.558%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.599%
2011-01-23T12:19:00	markr	tiny	120000	2340000		-		-	-	0.023	-	-	2.860%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	149733	149733		-		-	-	0.014	-	-	1.154%
2016-03-31T11:12:56	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.170%

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	-	-
2022-03-09T10:13:26	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.071	-	-
2009-01-04T06:36:00	Sturle Sunde	gibsy.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-06T21:57:00	Sturle Sunde	ghia.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-09-08T17:50:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.455	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.909	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.731	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.135 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	2.135 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	0.962	38.230%
25	50000	0.089	91.487%
30	250000	0.006	99.440%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	1.879
50000	5000000	2194433765487885130303	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-19T13:19:00	NeedGem Liou	FakeServer	50000	5000000						3	0.256
2009-11-29T21:47:00	SubPrime	mysql0	50000	5000000						3	0.256
2011-08-18T03:53:00	Csaba Vágó	debws-0759	50000	5000000						3	0.256
2013-05-02T09:31:00	hiems	Laptop	50000	5000000						3	0.256
2015-01-19T07:19:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-09-18T13:41:00	lopper	i5-4670	50000	5000000	2194433765487885130303	70.894	3	2		3	0.256
2022-07-20T02:24:27	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.598

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	CD4210697129AA2A	0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:35

alpertron

Manual testing

2194433765487885130303

457B2BA621630F__

2017-10-21T22:42:19

Oliver Kruse

Threadripper

2194433765487885130303

457B2BA621630F__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 120000, B2 = 2340000 (P-1 stage 2)

B1 = 149733 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 45000 (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)

10¹

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10⁴

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10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-07-20T02:24:27+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