M2392571 Mersenne number exponent details

≡

M2392571

<<<

>>>

is 2 ^2392571 - 1

has 720236 decimal digits

takes 0.162 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	D6F38FDF35482740	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	12.4192	67.1642%	2000000	60000000	0.5055	7.6128%	12.9247	69.6639%	2.4997%
PrimeNet	2⁵⁹	0.0321	62.7119%	10000	170000	0.0018	2.4782%	0.0339	63.6359%	0.9241%
GPU72	2⁶³	0.6671	65.0794%	10000	140000	0.0017	1.2740%	0.6687	65.5243%	0.4449%
Difference	+4	+11.7522	+2.0848%	+1990000	+59860000	+0.5038	+6.3388%	+12.2559	+4.1397%	+4.1397%

Known prime factors (1 factor, 70.2 bits, 0.00293580% 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
2392571	1395268819057691277839	22	70.241	291583576633189 41 × 194521 × 36560549	2015-06-26	194521	36560549	158.04	0.2131	0.3644

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.003	-	-	0.572%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2010-12-16T22:39:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.311%
2011-01-01T10:27:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.793%
2011-01-22T16:24:00	Oscar Östlin		90000	1845000		-		-	-	0.018	-	-	2.603%
2014-08-21T02:33:00	Jocelyn Larouche	Manual testing	116826	116826		-		-	-	0.011	-	-	1.027%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	143652	143652		-		-	-	0.014	-	-	1.150%
2018-09-28T16:25:14	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 1395268819057691277839	-	-	0.505	-	-	7.613%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:57	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-17T18:25:00	Sturle Sunde	gassmann.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-02T07:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.128	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.410	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.821	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.562	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.246 GHz-days
Estimated T-Level:	0.700

Digits	B1	Curves	Complete	FacMiss
20	11000	14 / 100	0.140	86.875%
25	50000	14 / 280	0.050	95.114%

New Calculation Method

Total ECM effort:	1.246 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.452	63.660%
25	50000	0.041	96.001%
30	250000	0.003	99.749%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.068
50000	5000000	1395268819057691277839	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-30T06:37:00	Lauri Mukkala	Toveri	50000	5000000						3	0.267
2010-02-15T00:29:00	ashon	Aaron-Quad	50000	5000000						3	0.267
2012-02-15T11:01:00	Emiel	SlimLine	50000	5000000						3	0.267
2013-11-25T06:58:00	Andy Incline	Office-PC	50000	5000000						3	0.267
2015-06-26T11:35:00	guru	w6	50000	5000000	1395268819057691277839	70.241	2	2		2	0.178

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-23T00:00:00	ANONYMOUS	v4_computers	D6F38FDF35482740	0.162
1999-03-26T00:00:00	ANONYMOUS	v4_computers	D6F38FDF35482740	0.162

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T20:16:12

Oliver Kruse

GTX-0

58693E6B405356__

2017-11-26T01:13:40

kkmrkkblmbrbk

c4.xlarge

1395268819057691277839

58693E6B405356__

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 = 90000, B2 = 1845000 (P-1 stage 2)

B1 = 143652 (P-1 stage 1)

B1 = 116826 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 4096 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-09T16:37:57+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