M2692247 Mersenne number exponent details

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M2692247

<<<

>>>

is 2 ^2692247 - 1

has 810448 decimal digits

takes 0.208 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	2F028245E60BFE82	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	11.0368	67.1642%	2000000	60000000	0.5779	7.7054%	11.6147	69.6943%	2.5301%
PrimeNet	2⁵⁹	0.0285	62.7119%	12000	220000	0.0026	2.8416%	0.0311	63.7714%	1.0596%
GPU72	2⁶³	0.5928	65.0794%	14000	220000	0.0028	1.6604%	0.5956	65.6592%	0.5798%
Difference	+4	+10.4440	+2.0848%	+1986000	+59780000	+0.5751	+6.0450%	+11.0191	+4.0351%	+4.0351%

Known prime factors (1 factor, 71.6 bits, 0.00265925% 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
2692247	3563151551277546570967	22	71.594	661743062816589 3² × 13 × 5655923613817	2018-06-22	13	5655923613817	191.76	34,510	64,456

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.297%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.920%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.319%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.438%
2011-01-31T19:56:00	markr	tiny	105000	2310000		-		-	-	0.025	-	-	2.875%
2016-07-14T05:43:48	Jocelyn Larouche	Manual testing	167500	4620000	6	-		-	-	0.046	-	-	3.627%
2016-12-21T00:33:41	Jocelyn Larouche	low 4M	201000	201000		-		-	-	0.023	-	-	1.395%
2017-04-22T17:25:07	Jocelyn Larouche	low 4M	335000	3350000	6	-		-	-	0.056	-	-	3.713%
2019-07-04T12:48:54	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.578	-	-	7.705%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-26T22:00:00	Sturle Sunde	gicy.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-05T03:31:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.365	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.729	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.388	-	-
2016-01-27T13:46:24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.776	-	-
2017-09-15T16:43:52	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.551	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.106 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	3.106 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	0.968	37.994%
25	50000	0.087	91.625%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.795
50000	5000000	3563151551277546570967	3	0.311

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-09T21:21:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.311
2010-08-03T23:30:00	James Classen	towerofart	50000	5000000						3	0.311
2012-12-30T09:52:00	Brian V.	dxl5420	50000	5000000						3	0.311
2015-01-08T13:31:00	arnaud	srv-630	50000	5000000						3	0.311
2016-04-12T04:47:25	Jason U	Server7	50000	5000000						3	0.311
2016-04-24T23:52:45	AnthonyRais	Main	50000	5000000						3	0.311
2016-11-04T04:44:11	lettp	Home	50000	5000000						3	0.311
2017-07-10T23:00:15	Bruce	eleven	50000	5000000						3	0.311
2017-11-21T15:44:47	Yan Jinzhao	cndns	50000	5000000						3	0.311
2018-06-22T04:49:27	Chang Chia-Tche	ex-ctcpc	50000	5000000	3563151551277546570967	71.594	3	2		3	0.311

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	curtisc	v4_computers	2F028245E60BFE82	0.208

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-06-22T09:57:01

Anton Repko

Manual testing

3563151551277546570967

0B40D2DD2F9EA7__

2018-06-22T23:51:18

GunnarLu

Ribenboim

3563151551277546570967

0B40D2DD2F9EA7__

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 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 335000, B2 = 3350000 (P-1 stage 2)

B1 = 167500, B2 = 4620000 (P-1 stage 2)

B1 = 335000 (P-1 stage 1)

B1 = 105000, B2 = 2310000 (P-1 stage 2)

B1 = 201000 (P-1 stage 1)

B1 = 167500 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (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

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10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-04T12:48:54+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