M3245201 Mersenne number exponent details

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M3245201

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>>>

is 2 ^3245201 - 1

has 976903 decimal digits

takes 0.276 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	8A045EA33ED65201	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	18.3671	67.6471%	4000000	150000000	1.4753	8.7725%	19.8424	70.4852%	2.8382%
PrimeNet	2⁶⁰	0.0473	63.3333%	14000	260000	0.0034	2.7701%	0.0507	64.3490%	1.0157%
GPU72	2⁶⁴	1.0968	65.6250%	16000	280000	0.0037	1.6544%	1.1005	66.1937%	0.5687%
Difference	+4	+17.2703	+2.0221%	+3984000	+149720000	+1.4716	+7.1182%	+18.7419	+4.2915%	+4.2915%

Known prime factors (1 factor, 95.8 bits, 0.00295183% 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
3245201	68627362943103954226265595703	29	95.793	10573669079835725772651 3 × 149 × 72701 × 2418517 × 134532949	2020-06-28	2418517	134532949	4.683e+9	1.1868	1.6895

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04T06:45:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.003	-	-	0.785%
2011-09-09T18:47:00	harlee	P4_2600	55000	866250		-		-	-	0.012	-	-	1.797%
2012-06-23T18:55:00	c10ck3r	Manual testing	1000000	30000000		-		-	-	0.318	-	-	6.031%
2020-06-28T11:22:08	mikr	MSI	4000000	150000000	12		68627362943103954226265595703	29	95.793	1.475	0.552	2.951	8.773%
2021-01-14T13:16:35	Jocelyn Larouche	Manual testing	324520	324520		-		-	-	0.040	-	-	1.595%
2021-01-16T17:21:44	Jocelyn Larouche	Manual testing	324520	3245201	6	-		-	-	0.060	-	-	3.389%
2022-01-06T11:34:10	Jocelyn Larouche	Manual testing	1561300	116447100		-		-	-	0.965	-	-	7.833%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-04T22:21:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-07-24T20:30:00	Carsten Kossendey	Manual testing	2⁶¹	2⁶²		-	-	0.095	-	-
2012-09-24T04:51:00	Richard B. Woods	Puttputt	2⁶²	2⁶³		-	-	0.302	-	-
2012-11-02T13:27:00	Richard B. Woods	Puttputt	2⁶³	2⁶⁴		-	-	0.605	-	-
2013-11-15T13:12:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	1.151	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.303	-	-
2017-03-27T22:26:22	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.605	-	-
2018-11-05T15:44:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.211	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.766 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.766 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.766

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-17T01:18:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.353
2011-09-16T19:04:00	Pool Party	desk_2	50000	5000000						3	0.353
2014-05-30T18:24:00	Bruce	fx6840-21	50000	5000000						3	0.353
2016-08-23T13:40:31	Dennis Schreiber	z400	50000	5000000						3	0.353
2018-12-05T20:15:22	nokno	leo234	50000	5000000						3	0.353

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-24T00:00:00	ANONYMOUS	v4_computers	8A045EA33ED65201	0.276
1998-07-05T00:00:00	ANONYMOUS	v4_computers	8A045EA33ED65201	0.276
1999-06-15T00:00:00	ANONYMOUS	v4_computers	8A045EA33ED65201	0.276

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-02T14:57:52

mnd9

mnd

68627362943103954226265595703

C6993C94B64BD3F8

2020-08-08T09:50:09

Justine V.

Gible_Desktop_1

68627362943103954226265595703

C6993C94B64BD3F8

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1561300, B2 = 116447100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1561300 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 324520, B2 = 3245201 (P-1 stage 2)

B1 = 324520 (P-1 stage 1)

B1 = 55000, B2 = 866250 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-06T11:34:10+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