M3220831 Mersenne number exponent details

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M3220831

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>>>

is 2 ^3220831 - 1

has 969567 decimal digits

takes 0.274 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	B76C87396610B0DD	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	18.5061	67.6471%	4000000	150000000	1.4753	8.7663%	19.9814	70.4832%	2.8362%
PrimeNet	2⁶⁰	0.0477	63.3333%	13000	240000	0.0031	2.6606%	0.0508	64.3089%	0.9755%
GPU72	2⁶⁴	1.1051	65.6250%	16000	260000	0.0036	1.6177%	1.1087	66.1811%	0.5561%
Difference	+4	+17.4010	+2.0221%	+3984000	+149740000	+1.4717	+7.1486%	+18.8727	+4.3021%	+4.3021%

Known prime factors (1 factor, 94.9 bits, 0.00294758% 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
3220831	37910299398474486087399437999	29	94.937	5885173639733734257929 2707 × 37339 × 2453707 × 23729339	2020-03-07	2453707	23729339	1.998e+9	0.4459	0.6163

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T00:38:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.003	-	-	0.784%
2011-09-04T18:44:00	harlee	P4_2600	60000	1035000		-		-	-	0.014	-	-	1.919%
2014-06-09T10:17:00	Jocelyn Larouche	Manual testing	79928	79928		-		-	-	0.010	-	-	0.754%
2014-09-29T22:05:00	Jocelyn Larouche	Manual testing	99856	99856		-		-	-	0.012	-	-	0.861%
2015-12-15T05:38:31	Squeeky_Squirrel	P4_2600	155000	3952500	6	-		-	-	0.045	-	-	3.181%
2016-04-19T21:44:55	Jocelyn Larouche	Manual testing	435425	12936633	6	-		-	-	0.138	-	-	4.710%
2020-03-07T09:45:16	mikr	MSI	4000000	150000000	12		37910299398474486087399437999	29	94.937	1.475	0.548	2.951	8.766%
2021-01-18T13:43:04	Jocelyn Larouche	Manual testing	465425	3220831	6	-		-	-	0.076	-	-	3.513%
2022-01-02T21:52:47	Jocelyn Larouche	Manual testing	3220831	3220831		-		-	-	0.397	-	-	3.814%
2022-01-03T11:28:02	Jocelyn Larouche	Manual testing	3220831	116701200		-	skipped known factor: 37910299398474486087399437999	-	-	1.161	-	-	8.315%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-05T06:44:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-03T20:15:00	markr	Manual testing	2¹	2⁶²		-	-	0.191	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.305	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.610	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.160	-	-
2015-06-24T21:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.320	-	-
2021-02-21T11:36:41	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.320	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.640	-	-
2017-03-20T00:06:22	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.640	-	-
2018-12-24T09:14:04	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.281	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.764 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:	1.764 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	1.764

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-13T01:06:00	TeamResslerTUB	1062320	50000	5000000						3	0.353
2011-09-12T14:51:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.353
2014-05-12T20:48:00	Lukasz Wrobel	w1	50000	5000000						3	0.353
2016-08-06T09:55:13	ANONYMOUS	PD925	50000	5000000						3	0.353
2018-10-01T15:35:29	IanGlencross	glenx24	50000	5000000						3	0.353

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	B76C87396610B0DD	0.274

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-03-07T10:07:32

mikr

V211

37910299398474486087399437999

2961C10EB997F875

2020-03-08T00:32:31

Niels_Mache_Nextcloud

SuperDry-X

37910299398474486087399437999

2961C10EB997F875

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 = 3220831, B2 = 116701200 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3220831 (P-1 stage 1)

B1 = 435425, B2 = 12936633 (P-1 stage 2)

B1 = 465425, B2 = 3220831 (P-1 stage 2)

B1 = 465425 (P-1 stage 1)

B1 = 435425 (P-1 stage 1)

B1 = 155000, B2 = 3952500 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

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

B1 = 99856 (P-1 stage 1)

B1 = 79928 (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: 2022-01-03T11:28:02+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