M3269081 Mersenne number exponent details

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M3269081

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>>>

is 2 ^3269081 - 1

has 984092 decimal digits

takes 0.343 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	-unknown-	-unknown-
PRP	D0C0CB233A0D2138	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	18.2329	67.6471%	4000000	150000000	1.8206	8.7786%	20.0535	70.4872%	2.8401%
PrimeNet	2⁶⁰	0.0470	63.3333%	14000	260000	0.0042	2.7738%	0.0512	64.3504%	1.0170%
GPU72	2⁶⁴	1.0888	65.6250%	17000	280000	0.0048	1.6862%	1.0936	66.2046%	0.5796%
Difference	+4	+17.1441	+2.0221%	+3983000	+149720000	+1.8158	+7.0924%	+18.9599	+4.2826%	+4.2826%

Known prime factors (1 factor, 81.3 bits, 0.00248682% 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
3269081	2968716720867666105012241	25	81.296	454059829179464520 2³ × 3 × 5 × 379 × 9983725355749	2021-01-21	379	9983725355749	210,120	82,837	154,716

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08T05:50:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.786%
2011-09-18T03:33:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.930%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	79634	79634		-		-	-	0.012	-	-	0.754%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99268	99268		-		-	-	0.015	-	-	0.861%
2016-01-16T00:42:30	Jocelyn Larouche	Manual testing	378000	3780000	6	-		-	-	0.086	-	-	3.580%
2020-11-27T15:41:01	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.779%
2022-04-05T14:54:04	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.647%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:33:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-26T23:16:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.094	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.300	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.601	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.143	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.286	-	-
2017-04-04T13:00:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.572	-	-
2018-12-17T13:21:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.144	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.067 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:	4.067 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.980	37.542%
25	50000	0.096	90.809%
30	250000	0.007	99.350%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.183
50000	6800000		3	0.507
80000	11280000		1	0.276
80000	11280000	2968716720867666105012241	4	1.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-23T09:01:00	TeamResslerTUB	1062319	50000	5000000						3	0.437
2011-09-20T10:05:00	Huaiyu Wu	eight	50000	5000000						3	0.437
2014-07-04T21:20:00	exhopp	9007	50000	5000000						3	0.437
2016-09-04T15:41:35	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-01-14T22:33:50	volki	home	50000	5000000						3	0.437
2020-12-30T07:12:56	axn	Manual testing	50000	6800000						3	0.507
2021-01-21T03:05:13	axn	Manual testing	80000	11280000	2968716720867666105012241	81.296	4	2	1051236574256517	4	1.102
2021-01-21T03:05:13	axn	Manual testing	80000	11280000						1	0.276

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-11-17T00:00:00	ANONYMOUS	v4_computers	D91A6669A06E49__	0.343

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-21T16:04:30

mrh

2968716720867666105012241

D0C0CB233A0D2138

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 = 1000000, B2 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 378000, B2 = 3780000 (P-1 stage 2)

B1 = 378000 (P-1 stage 1)

B1 = 60000, B2 = 1050000 (P-1 stage 2)

B1 = 99268 (P-1 stage 1)

B1 = 79634 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-05T14:54:04+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