M3115933 Mersenne number exponent details

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M3115933

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>>>

is 2 ^3115933 - 1

has 937990 decimal digits

takes 0.265 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	432F1DCEFFC26F8D	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	2⁶⁹	38.3149	68.1159%	3115933	668354610	4.8575	9.7046%	43.1724	71.2102%	3.0942%
PrimeNet	2⁶⁰	0.0493	63.3333%	13000	240000	0.0031	2.6446%	0.0524	64.3030%	0.9697%
GPU72	2⁶⁴	1.1423	65.6250%	14000	240000	0.0032	1.5086%	1.1455	66.1436%	0.5186%
Difference	+5	+37.1726	+2.4909%	+3101933	+668114610	+4.8542	+8.1960%	+42.0269	+5.0666%	+5.0666%

Known prime factors (1 factor, 95.6 bits, 0.00306848% 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
3115933	60540692088291724805445419633	29	95.612	9714697345593073536152 2³ × 661 × 94441 × 294509 × 66050891	2018-10-12	294509	66050891	4.800e+9	0.4785	0.8295

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	-	-	0.202%
2009-07-03T00:39:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.651%
2011-08-25T22:19:00	Squeeky_Squirrel	T7500_2200	105000	2126250		-		-	-	0.027	-	-	2.277%
2016-09-28T22:16:06	Squeeky_Squirrel	i5-5250U_1600	195000	5460000	12	-		-	-	0.059	-	-	3.161%
2016-10-03T01:22:51	Jocelyn Larouche	low 4M	105000	2551500	6	-		-	-	0.029	-	-	2.377%
2018-07-16T23:48:56	Jocelyn Larouche	low 4M	780000	2340000	6	-		-	-	0.107	-	-	3.017%
2018-07-17T07:39:18	Jocelyn Larouche	low 4M	780000	3120000	4	-		-	-	0.112	-	-	3.271%
2018-10-12T08:27:30	mikr	MSI	3000000	100000000	12		60540692088291724805445419633	29	95.612	1.022	0.530	2.045	7.422%
2020-12-25T17:15:25	Jocelyn Larouche	Manual testing	1537128	31159330	12	-		-	-	0.389	-	-	5.754%
2021-08-06T11:21:40	Jocelyn Larouche	Manual testing	3115933	3115933		-		-	-	0.385	-	-	3.410%
2021-12-08T12:48:17	Jocelyn Larouche	Manual testing	3115933	31159330	12	-		-	-	0.573	-	-	6.070%
2021-12-21T19:29:55	Jocelyn Larouche	Manual testing	3115933	139916700		-	skipped known factor: 60540692088291724805445419633	-	-	1.304	-	-	7.842%
2021-12-22T09:19:43	Jocelyn Larouche	Manual testing	3115933	668354610		-	skipped known factor: 60540692088291724805445419633	-	-	4.857	-	-	9.705%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-14T04:50:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-25T11:48:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.315	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.630	-	-
2021-01-02T01:34:49	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵		-	-	1.199	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.199	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.398	-	-
2021-01-03T02:39:40	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.398	-	-
2017-04-14T16:24:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.796	-	-
2021-02-25T15:38:25	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.59	-	-
2022-01-09T02:58:42	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.19	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.754 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:	1.754 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	1.754

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-24T00:55:00	borkencode	CFF2DC1CD	50000	5000000						3	0.351
2011-07-24T18:27:00	CuBr	H0E2035EE	50000	5000000						3	0.351
2013-12-09T03:09:00	Ryan Schulz	wenn	50000	5000000						3	0.351
2016-05-21T22:12:52	deo2016	deo2016.home2	50000	5000000						3	0.351
2017-11-24T09:29:46	Claude Portenier	Petit-Idiot	50000	5000000						3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	432F1DCEFFC26F8D	0.265
1999-06-15T00:00:00	ANONYMOUS	v4_computers	432F1DCEFFC26F8D	0.265

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-10-23T10:04:06

Hazar Temizel

60540692088291724805445419633

B18B94F64D82D3__

2018-10-24T20:26:27

arnaud

stm-11-010

60540692088291724805445419633

B18B94F64D82D3__

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 = 3115933, B2 = 668354610 (P-1 stage 2)

B1 = 3115933, B2 = 139916700 (P-1 stage 2)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3115933, B2 = 31159330 (P-1 stage 2)

B1 = 1537128, B2 = 31159330 (P-1 stage 2)

B1 = 3115933 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 1537128 (P-1 stage 1)

B1 = 780000, B2 = 3120000 (P-1 stage 2)

B1 = 780000, B2 = 2340000 (P-1 stage 2)

B1 = 780000 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 105000, B2 = 2551500 (P-1 stage 2)

B1 = 105000, B2 = 2126250 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 105000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-09T02:58:42+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