M2873491 Mersenne number exponent details

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M2873491

<<<

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is 2 ^2873491 - 1

has 865007 decimal digits

takes 0.222 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	1A28F6D55B5D5A9F	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	20.7430	67.6471%	5000000	200000000	1.7498	9.1803%	22.4928	70.6172%	2.9701%
PrimeNet	2⁵⁹	0.0267	62.7119%	13000	240000	0.0028	2.9972%	0.0296	63.8295%	1.1176%
GPU72	2⁶³	0.5554	65.0794%	16000	280000	0.0034	1.8700%	0.5588	65.7324%	0.6530%
Difference	+5	+20.1876	+2.5677%	+4984000	+199720000	+1.7464	+7.3103%	+21.9340	+4.8848%	+4.8848%

Known prime factors (1 factor, 73.5 bits, 0.00255873% 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
2873491	13589016588328171596889	23	73.525	2364548312197284 2² × 3 × 31 × 6356312667197	2020-08-12	31	6356312667197	729.67	38,784	72,438

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.245%
2009-07-03T00:55:00	Carsten Kossendey	leela	15000	161250		-		-	-	0.003	-	-	0.723%
2010-12-23T00:29:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.376%
2011-01-22T13:10:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.544%
2011-02-06T11:32:00	markr	tiny	200000	5250000		-		-	-	0.053	-	-	3.470%
2017-08-19T15:19:08	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.590%
2019-10-21T02:06:05	masser	Manual testing	2880000	28800000	12	-		-	-	0.481	-	-	6.428%
2020-03-01T15:03:12	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.180%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.027	-	-
2016-02-23T16:29:23	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.027	-	-
2009-02-13T21:07:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2012-01-28T19:05:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-07T13:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.342	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.683	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.300	-	-
2016-02-18T12:13:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.601	-	-
2017-11-12T17:07:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.201	-	-
2019-01-09T01:10:00	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.406 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	2.406 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.742	47.619%
25	50000	0.067	93.514%
30	250000	0.004	99.588%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	2.197
50000	5000000	13589016588328171596889	2	0.209

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-24T09:07:00	James Hintz	03_061809	50000	5000000						3	0.314
2011-01-05T00:13:00	Martti Järvi	Tiny	50000	5000000						3	0.314
2013-04-24T22:59:00	Richard Kint	xps	50000	5000000						3	0.314
2015-07-16T01:41:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2015-07-16T02:45:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2019-06-10T14:27:50	Claude Portenier	Petit-Idiot	50000	5000000						3	0.314
2020-08-04T15:18:54	GAN	LMS-15	50000	5000000						3	0.314
2020-08-12T16:41:14	GAN	LMS-11	50000	5000000	13589016588328171596889	73.525	2	2	3152351964379192	2	0.209

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-30T00:00:00	ANONYMOUS	v4_computers	1A28F6D55B5D5A9F	0.222
1999-09-22T00:00:00	ANONYMOUS	v4_computers	1A28F6D55B5D5A9F	0.222
2018-09-22T10:25:12	kkmrkkblmbrbk	old	1A28F6D55B5D5A9F	0.222

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-17T19:16:57

atrench

Desktop

13589016588328171596889

8E6810E04EBA39C6

2020-08-23T10:23:47

oodaira

com1

13589016588328171596889

8E6810E04EBA39C6

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2880000, B2 = 28800000 (P-1 stage 2)

B1 = 2880000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 200000, B2 = 5250000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 161250 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-23T10:23:47+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