M2270117 Mersenne number exponent details

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is 2 ^2270117 - 1

has 683374 decimal digits

takes 0.149 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	621C8816B3CE2BD3	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	2⁶⁸	26.2563	67.6471%	3000000	90000000	0.7379	7.6746%	26.9942	70.1300%	2.4830%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9210%	0.0188	63.1769%	1.1080%
GPU72	2⁶²	0.2706	64.5161%	12000	190000	0.0021	1.7077%	0.2727	65.1221%	0.6060%
Difference	+6	+25.9857	+3.1309%	+2988000	+89810000	+0.7358	+5.9668%	+26.7215	+5.0079%	+5.0079%

Known prime factors (1 factor, 86.3 bits, 0.00380054% 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
2270117	93722581640120475303610177	26	86.277	20642676487626072864 2⁵ × 3 × 29² × 137 × 17569 × 106226083	2020-07-06	17569	106226083	9,180,593	0.5533	1.0305

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.228%
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-12T22:13:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.357%
2011-01-02T21:05:00	markr	tiny	100000	2100000		-		-	-	0.020	-	-	2.413%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128274	128274		-		-	-	0.012	-	-	0.933%
2016-01-04T02:12:25	Jocelyn Larouche	Manual testing	216000	2160000	6	-		-	-	0.031	-	-	2.770%
2016-08-01T15:21:51	Jocelyn Larouche	Manual testing	216000	4320000	6	-		-	-	0.042	-	-	3.261%
2017-09-05T23:15:03	Jocelyn Larouche	low 4M	432000	4320000	6	-		-	-	0.061	-	-	3.575%
2019-11-19T20:08:21	BigBrother	Winston	3000000	90000000	12	-		-	-	0.738	-	-	7.675%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:10	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.068	-	-
2009-01-14T19:26:00	Sturle Sunde	gideon.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-06T10:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.432	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.865	-	-
2015-03-10T10:45:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.646	-	-
2015-10-31T16:44:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.292	-	-
2017-01-16T00:47:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.584	-	-
2019-04-29T13:20:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.17	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.706 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:	6.706 GHz-days
Estimated T-Level:	3.900

Digits	B1	Complete	FacMiss
20	11000	2.516	8.077%
25	50000	0.227	79.660%
30	250000	0.014	98.609%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	6.448
50000	5000000	93722581640120475303610177	3	0.258

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-08T00:00:00	ANONYMOUS	v4_computers	621C8816B3CE2BD3	0.149
2018-04-25T23:20:18	kkmrkkblmbrbk	old	621C8816B3CE2BD3	0.149

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-06T05:12:07

CrypticClue

cruncher

93722581640120475303610177

59F0804BB3EB0E8D

no

2020-07-08T23:44:03

nordi

sweet16

93722581640120475303610177

59F0804BB3EB0E8D

no

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 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 432000, B2 = 4320000 (P-1 stage 2)

B1 = 216000, B2 = 4320000 (P-1 stage 2)

B1 = 432000 (P-1 stage 1)

B1 = 216000, B2 = 2160000 (P-1 stage 2)

B1 = 216000 (P-1 stage 1)

B1 = 100000, B2 = 2100000 (P-1 stage 2)

B1 = 128274 (P-1 stage 1)

B1 = 100000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-08T23:44:03+00:00