M3165259 Mersenne number exponent details

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M3165259

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is 2 ^3165259 - 1

has 952838 decimal digits

takes 0.269 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	FA1F8864005E978E	double-checked
PRP	E757BF8636D26DC5	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	18.8310	67.6471%	3000000	100000000	1.0224	8.0644%	19.8534	70.2561%	2.6091%
PrimeNet	2⁶⁰	0.0485	63.3333%	13000	240000	0.0031	2.6522%	0.0517	64.3058%	0.9725%
GPU72	2⁶⁴	1.1245	65.6250%	15000	260000	0.0035	1.5815%	1.1280	66.1686%	0.5436%
Difference	+4	+17.7065	+2.0221%	+2985000	+99740000	+1.0189	+6.4829%	+18.7254	+4.0875%	+4.0875%

Known prime factors (1 factor, 70.6 bits, 0.00223030% 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
3165259	1782914197151501782297	22	70.595	281637963457572 2² × 3 × 17 × 199 × 6937579157	2021-01-31	199	6937579157	150.25	46.647	87.123

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.252%
2009-07-03T00:43:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.781%
2011-09-09T13:17:00	Squeeky_Squirrel	T7500_2200	60000	960000		-		-	-	0.013	-	-	1.876%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	80278	80278		-		-	-	0.010	-	-	0.753%
2014-09-25T21:11:00	Jocelyn Larouche	Manual testing	100556	100556		-		-	-	0.012	-	-	0.862%
2015-08-10T13:57:00	Jocelyn Larouche	Manual testing	433923	433923		-		-	-	0.054	-	-	1.811%
2015-11-06T02:59:21	Jocelyn Larouche	Manual testing	552052	552052		-		-	-	0.068	-	-	2.009%
2015-11-30T10:40:51	HBendtz	Manual testing	500000	12000000	12	-		-	-	0.139	-	-	4.711%
2019-07-25T02:55:07	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.064%
2022-02-22T08:54:57	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.621%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-07-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-08T17:57:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-10-30T07:39:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.097	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.310	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.620	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.180	-	-
2015-06-17T10:00:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.361	-	-
2017-04-22T18:10:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.722	-	-
2019-01-21T12:54:07	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.443	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.220 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	4.220 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	3.400
50000	5000000	1782914197151501782297	7	0.821

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-04T14:12:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.352
2011-08-09T14:12:00	Smurgs	Praca	50000	5000000						3	0.352
2014-03-21T12:32:00	Dougal	dougal	50000	5000000						3	0.352
2016-06-26T10:25:56	f0rteOC	Fortissimo	50000	5000000						3	0.352
2018-03-12T10:09:36	Aare Vesi	h1	50000	5000000						3	0.352
2020-11-27T09:42:21	mnd9	libproj	50000	5000000						7	0.821
2020-12-31T18:24:08	daveward2005	Dave2	50000	5000000						7	0.821
2021-01-31T06:16:29	MarkS	desktop-i7	50000	5000000	1782914197151501782297	70.595	7	2	6598129373937575	7	0.821

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-19T00:00:00	ANONYMOUS	v4_computers	FA1F8864005E978E	0.269
1999-06-26T00:00:00	ANONYMOUS	v4_computers	FA1F8864005E978E	0.269

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-31T12:39:48

ViliamF

1782914197151501782297

E757BF8636D26DC5

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 500000, B2 = 12000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 552052 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 433923 (P-1 stage 1)

B1 = 60000, B2 = 960000 (P-1 stage 2)

B1 = 100556 (P-1 stage 1)

B1 = 80278 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-22T08:54:57+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