M3231313 Mersenne number exponent details

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M3231313

<<<

>>>

is 2 ^3231313 - 1

has 972723 decimal digits

takes 0.275 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	0D84663DFF86D640	double-checked
PRP	CB06246583AB56E0	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	18.4460	67.6471%	4000000	150000000	1.4753	8.7690%	19.9213	70.4841%	2.8370%
PrimeNet	2⁶⁰	0.0475	63.3333%	14000	260000	0.0034	2.7680%	0.0509	64.3483%	1.0149%
GPU72	2⁶⁴	1.1015	65.6250%	16000	280000	0.0037	1.6530%	1.1053	66.1932%	0.5682%
Difference	+4	+17.3445	+2.0221%	+3984000	+149720000	+1.4716	+7.1160%	+18.8161	+4.2909%	+4.2909%

Known prime factors (1 factor, 75.4 bits, 0.00233226% 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
3231313	48572754076198988131537	23	75.363	7515946934914536 2³ × 3² × 17 × 389 × 15785294401	2020-12-27	389	15785294401	3,770.5	106.14	198.23

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T07:18:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.003	-	-	0.784%
2011-09-07T07:38:00	harlee	P4_2600	60000	1035000		-		-	-	0.014	-	-	1.920%
2014-06-11T02:09:00	Jocelyn Larouche	Manual testing	79863	79863		-		-	-	0.010	-	-	0.754%
2014-09-29T22:05:00	Jocelyn Larouche	Manual testing	99726	99726		-		-	-	0.012	-	-	0.861%
2016-01-10T19:08:48	Squeeky_Squirrel	P4_2600	165000	4413750	6	-		-	-	0.049	-	-	3.294%
2016-05-21T05:26:04	Jocelyn Larouche	Manual testing	377838	6801084	6	-		-	-	0.090	-	-	4.071%
2020-04-22T02:23:33	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.769%
2021-01-17T23:14:13	Jocelyn Larouche	Manual testing	407838	3231313	6	-		-	-	0.069	-	-	3.471%
2022-01-24T05:49:00	Jocelyn Larouche	Manual testing	1073130	119912100		-		-	-	0.931	-	-	7.572%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-05T22:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-09-24T16:22:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.095	-	-
2013-01-03T08:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.304	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.608	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.156	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.313	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.313	-	-
2021-02-22T09:03:46	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.625	-	-
2017-03-26T03:14:45	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.625	-	-
2018-12-03T19:08:44	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.250	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.984 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	2.984 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	0.813	44.347%
25	50000	0.073	92.915%
30	250000	0.005	99.548%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.765
50000	5000000	48572754076198988131537	7	0.824
50000	6350000		3	0.396

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-14T15:45:00	TeamResslerTUB	1062315	50000	5000000						3	0.353
2011-09-12T07:25:00	Pool Party	desk_1	50000	5000000						3	0.353
2014-05-19T15:07:00	Lukasz Wrobel	sr-1	50000	5000000						3	0.353
2016-08-12T11:57:06	Dennis Schreiber	z400	50000	5000000						3	0.353
2018-10-19T17:31:27	storm5510	7700_Kaby_Lake	50000	5000000						3	0.353
2020-12-27T01:03:20	daveward2005	Davy	50000	5000000	48572754076198988131537	75.363	7	2	6510130490679060	7	0.824
2021-01-01T01:57:34	axn	Manual testing	50000	6350000						3	0.396

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	Ernst W. Mayer	v4_computers	0D84663DFF86D640	0.275
1999-06-15T00:00:00	ANONYMOUS	v4_computers	0D84663DFF86D640	0.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-28T03:41:27

Niels_Mache_Nextcloud

conf4-a

48572754076198988131537

CB06246583AB56E0

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 = 1073130, B2 = 119912100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1073130 (P-1 stage 1)

B1 = 377838, B2 = 6801084 (P-1 stage 2)

B1 = 407838, B2 = 3231313 (P-1 stage 2)

B1 = 407838 (P-1 stage 1)

B1 = 165000, B2 = 4413750 (P-1 stage 2)

B1 = 377838 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

B1 = 60000, B2 = 1035000 (P-1 stage 2)

B1 = 99726 (P-1 stage 1)

B1 = 79863 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-24T05:49:00+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