M3126001 Mersenne number exponent details

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M3126001

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>>>

is 2 ^3126001 - 1

has 941021 decimal digits

takes 0.266 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	5697DA07D5921FB2	double-checked
PRP	E8C35A446AF45D72	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	19.0675	67.6471%	3000000	100000000	1.0224	8.0545%	20.0899	70.2529%	2.6059%
PrimeNet	2⁶⁰	0.0491	63.3333%	13000	240000	0.0031	2.6462%	0.0523	64.3036%	0.9703%
GPU72	2⁶⁴	1.1386	65.6250%	15000	240000	0.0034	1.5419%	1.1420	66.1550%	0.5300%
Difference	+4	+17.9288	+2.0221%	+2985000	+99760000	+1.0191	+6.5126%	+18.9479	+4.0979%	+4.0979%

Known prime factors (1 factor, 71.0 bits, 0.00227011% 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
3126001	2302472411008737060913	22	70.964	368277619074456 2³ × 3 × 7 × 13 × 168625283459	2020-11-14	13	168625283459	109.82	1,133.8	2,117.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.251%
2009-08-13T12:59:00	Carsten Kossendey	durandal	15000	180000		-		-	-	0.003	-	-	0.763%
2011-08-31T03:55:00	Squeeky_Squirrel	T7500_2200	95000	1757500		-		-	-	0.023	-	-	2.404%
2016-04-12T10:52:11	Jocelyn Larouche	Manual testing	190000	5809400	6	-		-	-	0.061	-	-	3.556%
2016-04-14T09:31:27	harlee	P4_2600	215000	6073750	12	-		-	-	0.066	-	-	3.660%
2018-08-18T21:36:22	Jocelyn Larouche	low 4M	430000	2580000		-		-	-	0.068	-	-	3.283%
2018-08-19T12:41:38	Jocelyn Larouche	low 4M	430000	3440000		-		-	-	0.073	-	-	3.529%
2018-08-19T20:22:25	Jocelyn Larouche	low 4M	430000	3870000		-		-	-	0.076	-	-	3.630%
2018-08-20T10:36:02	Jocelyn Larouche	low 4M	430000	4300000		-		-	-	0.079	-	-	3.720%
2018-12-11T06:31:57	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.054%
2021-01-17T00:34:25	Jocelyn Larouche	Manual testing	460000	3126001	6	-		-	-	0.075	-	-	3.470%
2022-01-24T00:01:10	Jocelyn Larouche	Manual testing	1072600	119912100		-		-	-	0.931	-	-	7.545%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-13T07:55:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-07-05T23:23:00	Rob_Dee	twopc	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.314	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.628	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.195	-	-
2015-06-14T13:51:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.391	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.391	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.781	-	-
2017-04-16T02:34:53	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.781	-	-
2019-01-14T11:03:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.56	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.105 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	2.105 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.692	50.042%
25	50000	0.064	93.795%
30	250000	0.004	99.597%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.755
50000	5000000	2302472411008737060913	3	0.351

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-07T02:59:00	Marzbug	Xeon	50000	5000000						3	0.351
2011-07-29T02:14:00	Csaba Vágó	apugep	50000	5000000						3	0.351
2013-12-25T21:26:00	Bruce	apandya-DESK11	50000	5000000						3	0.351
2016-05-30T12:38:48	arnaud	PORTABLE08	50000	5000000						3	0.351
2017-12-20T09:42:13	Claude Portenier	Petit-Idiot	50000	5000000						3	0.351
2020-11-14T19:17:01	rextherunt	ice	50000	5000000	2302472411008737060913	70.964	3	2		3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	5697DA07D5921FB2	0.266
1999-09-22T00:00:00	ANONYMOUS	v4_computers	5697DA07D5921FB2	0.266

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-11-17T11:09:18

arnaud

SRV-130

2302472411008737060913

E8C35A446AF45D72

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1072600, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1072600 (P-1 stage 1)

B1 = 430000, B2 = 4300000 (P-1 stage 2)

B1 = 430000, B2 = 3870000 (P-1 stage 2)

B1 = 460000, B2 = 3126001 (P-1 stage 2)

B1 = 430000, B2 = 3440000 (P-1 stage 2)

B1 = 430000, B2 = 2580000 (P-1 stage 2)

B1 = 215000, B2 = 6073750 (P-1 stage 2)

B1 = 190000, B2 = 5809400 (P-1 stage 2)

B1 = 460000 (P-1 stage 1)

B1 = 430000 (P-1 stage 1)

B1 = 215000 (P-1 stage 1)

B1 = 190000 (P-1 stage 1)

B1 = 95000, B2 = 1757500 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

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10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-24T00:01:10+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