M27142097 Mersenne number exponent details

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is 2 ^27142097 - 1

has 8170586 decimal digits

takes 25.125 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 L-L tests remaining

	Residue	Status
L-L	D58E2A71178E4704	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	2⁷¹	17.6139	64.7887%	1350000	109350000	9.7101	7.4068%	27.3240	67.3968%	5.2756%
PrimeNet	2⁶⁶	0.5441	62.1212%	120000	4500000	0.4814	5.2124%	1.0255	64.0956%	1.9744%
GPU72	2⁷⁰	8.8037	64.2857%	200000	6000000	0.6926	3.9038%	9.4963	65.6799%	1.3942%
Difference	+1	+8.8102	+0.5030%	+1150000	+103350000	+9.0175	+3.5030%	+17.8277	+1.7168%	+1.7168%

Known prime factors (2 factors, 174.1 bits, 0.00064160% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27142097	101506090449946597475449391	27	86.392	1869901401685112935 5 × 97 × 6163 × 34297 × 18240161	2021-03-18	34297	18240161	1,056,667	1.3774	2.4914
27142097	260439669432425817621061183	27	87.751	4797707219018961903 3² × 17 × 349 × 547 × 66067 × 2486251	2021-03-18	66067	2486251	1,530,448	0.2657	0.3396

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
27142097	101506090449946597475449391 260439669432425817621061183	26436212642162007070517822654531755460254859231089 553	53	174.143

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2005-01-10T00:00:00	ANONYMOUS	v4_computers	420000	420000		-		-	-	0.564	-	-	1.736%
2021-03-18T10:52:00	firejuggler	Maison	1350000	109350000			101506090449946597475449391 260439669432425817621061183	53	174.143	9.71	50.25	19.42	7.407%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-14T20:10:25	firejuggler	Maison	500000	23000000	6	5			-	-	2.633

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-18T00:00:00	Net_Force	v4_computers	?	2⁵⁶		-	-	0.000	-	-
2002-08-31T00:00:00	Jocelyn Larouche	v4_computers	?	2⁵⁷		-	-	0.001	-	-
2004-03-16T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.011	-	-
2004-10-18T00:00:00	ANONYMOUS	v4_computers	?	2⁶⁷		-	-	0.551	-	-
2016-01-17T22:08:18	NR	Manual testing	2⁶⁷	2⁶⁸		-	-	1.101	-	-
2018-04-09T13:24:07	VictordeHollander	Manual testing	2⁶⁸	2⁶⁹		-	-	2.203	-	-
2018-09-11T02:25:23	chuenkit	Manual testing	2⁶⁹	2⁷⁰		-	-	4.405	-	-
2021-02-19T06:15:06	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	8.810	-	-

ECM factoring results:
Exponent "27142097" not found

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-05-12T00:00:00	ANONYMOUS	v4_computers	A7134B655E627C__	25.13
2007-01-16T00:00:00	Martin Winter	v4_computers	D58E2A71178E4704	25.13
2011-03-29T06:43:00	ANONYMOUS		D58E2A71178E4704	25.13

PRP results:
Exponent "27142097" not found

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 = 1350000, B2 = 109350000 (stage 2)

B1 = 1350000 (stage 1)

B1 = 420000 (stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶²

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-05-14T20:10:25+00:00