M2280071 Mersenne number exponent details

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is 2 ^2280071 - 1

has 686370 decimal digits

takes 0.150 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	F858AD31BB01278D	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	26.1417	67.6471%	519062	5190620	0.0738	3.8071%	26.2154	68.8788%	1.2317%
PrimeNet	2⁵⁸	0.0168	62.0690%	10000	190000	0.0019	2.9233%	0.0187	63.1778%	1.1088%
GPU72	2⁶²	0.2694	64.5161%	12000	190000	0.0021	1.7092%	0.2715	65.1226%	0.6065%
Difference	+6	+25.8722	+3.1309%	+507062	+5000620	+0.0717	+2.0979%	+25.9439	+3.7562%	+3.7562%

Known prime factors (1 factor, 76.5 bits, 0.00335370% 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
2280071	104425692125647222042919	24	76.467	22899657976801429 2271307 × 10082150047	2020-07-09	2271307	10082150047	10,706	52.574	97.811

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	-	-	0.229%
2010-11-07T01:16:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-14T20:17:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.258%
2010-11-24T12:47:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.678%
2011-01-14T14:34:00	Oscar Östlin		85000	1742500		-		-	-	0.017	-	-	2.233%
2014-06-11T02:09:00	Jocelyn Larouche	Manual testing	113150	113150		-		-	-	0.011	-	-	0.869%
2014-10-06T21:12:00	Jocelyn Larouche	Manual testing	141300	141300		-		-	-	0.013	-	-	0.986%
2016-01-23T12:46:39	Jocelyn Larouche	Manual testing	519062	5190620	6	-		-	-	0.074	-	-	3.807%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15T01:45:00	Sturle Sunde	gowin.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-09T17:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.431	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.861	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.639	-	-
2015-11-01T21:51:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.277	-	-
2017-02-13T09:31:36	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	6.555	-	-
2019-09-09T13:15:03	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	13.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.710 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:	6.710 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	6.452
50000	5000000	104425692125647222042919	3	0.258

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	F858AD31BB01278D	0.150
2018-04-27T09:21:06	kkmrkkblmbrbk	old	F858AD31BB01278D	0.150

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-09T05:38:48

CrypticClue

cruncher

104425692125647222042919

E064DA828F1DF59A

no

2020-07-09T20:11:53

pew

10980xe_1

104425692125647222042919

E064DA828F1DF59A

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 = 519062, B2 = 5190620 (P-1 stage 2)

B1 = 519062 (P-1 stage 1)

B1 = 85000, B2 = 1742500 (P-1 stage 2)

B1 = 141300 (P-1 stage 1)

B1 = 113150 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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)

10²

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

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2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-09T20:11:53+00:00