M2479691 Mersenne number exponent details

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M2479691

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is 2 ^2479691 - 1

has 746462 decimal digits

takes 0.172 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	6D420D211871B96F	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	11.9829	67.1642%	2382500	85770100	0.6965	8.1954%	12.6795	69.8552%	2.6910%
PrimeNet	2⁵⁹	0.0310	62.7119%	10000	180000	0.0019	2.5340%	0.0329	63.6567%	0.9449%
GPU72	2⁶³	0.6436	65.0794%	11000	160000	0.0019	1.3798%	0.6456	65.5612%	0.4818%
Difference	+4	+11.3393	+2.0848%	+2371500	+85610100	+0.6946	+6.8156%	+12.0339	+4.2940%	+4.2940%

Known prime factors (1 factor, 89.3 bits, 0.00360226% 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
2479691	775298271494443782853824911	27	89.325	156329613547503254005 5 × 7² × 53 × 281 × 251177 × 170574109	2014-10-29	251177	170574109	63,965,342	0.9586	1.7457

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.290%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.919%
2010-11-20T12:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.313%
2011-01-20T16:02:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.679%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	120884	120884		-		-	-	0.012	-	-	1.053%
2014-10-29T04:05:00	mikr	MSI	2382500	85770100	12		775298271494443782853824911	27	89.325	0.697	0.344	1.393	8.195%
2019-07-04T12:37:52	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.641%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
1999-06-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
1999-09-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:53:00	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-14T04:58:00	Sturle Sunde	scarpia.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-09T05:29:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-01-23T08:29:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.396	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-15T06:06:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.275
2010-04-09T09:41:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.275
2012-06-07T16:27:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.275
2014-02-03T04:38:00	arnaud	srv-630	50000	5000000						3	0.275

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	6D420D211871B96F	0.172
1999-06-26T00:00:00	ANONYMOUS	v4_computers	6D420D211871B96F	0.172
1999-09-14T00:00:00	ANONYMOUS	v4_computers	6D420D211871B96F	0.172

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T03:48:23

Oliver Kruse

GTX-0

3EA13A43ADE066__

2017-11-29T12:54:05

kkmrkkblmbrbk

c4.xlarge

775298271494443782853824911

3EA13A43ADE066__

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 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120884 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-10T05:53:00+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