M3211427 Mersenne number exponent details

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M3211427

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is 2 ^3211427 - 1

has 966736 decimal digits

takes 0.273 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	01B6FFBBF3D19E72	double-checked
PRP	3D79A7534AD13B52	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	18.5602	67.6471%	4000000	150000000	1.4753	8.7639%	20.0356	70.4824%	2.8354%
PrimeNet	2⁶⁰	0.0478	63.3333%	13000	240000	0.0031	2.6592%	0.0510	64.3084%	0.9750%
GPU72	2⁶⁴	1.1083	65.6250%	16000	260000	0.0036	1.6168%	1.1119	66.1808%	0.5558%
Difference	+4	+17.4519	+2.0221%	+3984000	+149740000	+1.4717	+7.1471%	+18.9236	+4.3017%	+4.3017%

Known prime factors (1 factor, 75.6 bits, 0.00235328% 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
3211427	56237428345782788363377	23	75.574	8755831651440744 2³ × 3⁴ × 13 × 1039391221681	2020-12-24	81	1039391221681	2,395.1	6,988.6	13,053

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T21:37:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.783%
2011-09-25T08:46:00	harlee	P4_2600	55000	852500		-		-	-	0.012	-	-	1.786%
2013-09-03T06:58:00	Squeeky_Squirrel	T7500_2200	115000	2587500		-		-	-	0.031	-	-	2.743%
2016-11-19T05:45:53	Squeeky_Squirrel	P4_2600	200000	5600000	12	-		-	-	0.061	-	-	3.571%
2018-07-24T12:57:27	Jocelyn Larouche	low 4M	400000	1044095		-		-	-	0.054	-	-	2.524%
2018-07-25T17:21:12	Jocelyn Larouche	low 4M	400000	2165034		-		-	-	0.061	-	-	3.125%
2018-07-27T18:51:12	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.074	-	-	3.642%
2020-01-26T11:37:17	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.764%
2021-01-17T23:14:13	Jocelyn Larouche	Manual testing	420000	3211427	6	-		-	-	0.071	-	-	3.474%
2022-01-24T00:02:04	Jocelyn Larouche	Manual testing	1071142	119912100		-		-	-	0.931	-	-	7.566%

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		-	-	0.048	-	-
2009-04-05T22:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-08-26T04:12:00	markr	Manual testing	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.306	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.611	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.163	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.327	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.327	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.654	-	-
2017-03-17T19:55:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.654	-	-
2019-01-14T11:03:49	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.308	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.881 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.881 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.516	59.683%
25	50000	0.047	95.442%
30	250000	0.003	99.713%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.763
50000	5000000	56237428345782788363377	1	0.118

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-15T01:31:00	Net_Force	Vista64	50000	5000000						3	0.353
2011-09-05T17:14:00	Pool Party	desk_1	50000	5000000						3	0.353
2014-05-09T21:10:00	Dougal	dougal	50000	5000000						3	0.353
2016-07-30T00:23:18	f0rteOC	Fortissimo	50000	5000000						3	0.353
2018-10-19T09:02:32	nokno	leo235	50000	5000000						3	0.353
2020-12-24T16:02:20	daveward2005	Dave2	50000	5000000	56237428345782788363377	75.574	1	2	6824297509490207	1	0.118

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	01B6FFBBF3D19E72	0.273
1999-10-15T00:00:00	ANONYMOUS	v4_computers	01B6FFBBF3D19E72	0.273

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-26T16:36:08

mrh

lanai

56237428345782788363377

3D79A7534AD13B52

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 = 1071142, B2 = 119912100 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1071142 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 420000, B2 = 3211427 (P-1 stage 2)

B1 = 400000, B2 = 2165034 (P-1 stage 2)

B1 = 200000, B2 = 5600000 (P-1 stage 2)

B1 = 400000, B2 = 1044095 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 115000, B2 = 2587500 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 55000, B2 = 852500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10⁰

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10³

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10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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10¹³

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-24T00:02:04+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