M3270257 Mersenne number exponent details

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M3270257

<<<

>>>

is 2 ^3270257 - 1

has 984446 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	6309EC1FB3530216	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	18.2264	67.6471%	4000000	150000000	1.8206	8.7789%	20.0469	70.4873%	2.8402%
PrimeNet	2⁶⁰	0.0470	63.3333%	14000	260000	0.0042	2.7739%	0.0511	64.3504%	1.0171%
GPU72	2⁶⁴	1.0884	65.6250%	17000	280000	0.0048	1.6863%	1.0932	66.2047%	0.5797%
Difference	+4	+17.1380	+2.0221%	+3983000	+149720000	+1.8158	+7.0926%	+18.9537	+4.2826%	+4.2826%

Known prime factors (1 factor, 86.5 bits, 0.00264657% 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
3270257	113243430192372015630188953	27	86.550	17314148428146781068 2² × 3 × 11² × 13 × 43 × 339727 × 62790313	2020-12-04	339727	62790313	8,078,149	0.5699	0.9731

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-08T12:40:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.786%
2011-09-18T12:04:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.938%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	79627	79627		-		-	-	0.012	-	-	0.754%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99254	99254		-		-	-	0.015	-	-	0.861%
2016-01-16T00:42:31	Jocelyn Larouche	Manual testing	383400	3834000	6	-		-	-	0.087	-	-	3.597%
2020-12-04T13:38:06	mikr	MSI	4000000	150000000	12		113243430192372015630188953	27	86.550	1.821	0.687	3.641	8.779%
2021-01-18T13:43:03	Jocelyn Larouche	Manual testing	403400	3270257	6	-		-	-	0.085	-	-	3.483%
2022-01-06T11:34:58	Jocelyn Larouche	Manual testing	1240536	116447100		-	skipped known factor: 113243430192372015630188953	-	-	1.145	-	-	7.664%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:32:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-12-13T02:08:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.094	-	-
2012-12-30T00:06:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.300	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.600	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.143	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.285	-	-
2021-02-21T11:36:43	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.285	-	-
2021-02-22T09:03:46	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.570	-	-
2017-04-04T13:00:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.570	-	-
2018-12-17T13:21:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.140	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.183 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:	2.183 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	2.183

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-31T06:57:00	KAMCOBILL	PC01	50000	5000000						3	0.437
2011-12-13T21:04:00	Huaiyu Wu	eight	50000	5000000						3	0.437
2014-07-03T10:50:00	fireredd	ont111	50000	5000000						3	0.437
2016-09-04T17:29:26	prime_dive	erazer	50000	5000000						3	0.437
2019-01-16T14:21:25	IanGlencross	glenx24	50000	5000000						3	0.437

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	F4AE910D051AC7__	0.343

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-04T18:50:17

mrh

113243430192372015630188953

6309EC1FB3530216

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 = 1240536, B2 = 116447100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1240536 (P-1 stage 1)

B1 = 383400, B2 = 3834000 (P-1 stage 2)

B1 = 403400, B2 = 3270257 (P-1 stage 2)

B1 = 403400 (P-1 stage 1)

B1 = 383400 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 99254 (P-1 stage 1)

B1 = 79627 (P-1 stage 1)

B1 = 60000 (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: 2022-01-06T11:34:58+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