M3039163 Mersenne number exponent details

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M3039163

<<<

>>>

is 2 ^3039163 - 1

has 914880 decimal digits

takes 0.259 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	8CEC2E0B0EFB07D2	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	19.6123	67.6471%	3000000	100000000	1.0224	8.0322%	20.6347	70.2457%	2.5986%
PrimeNet	2⁶⁰	0.0505	63.3333%	12000	220000	0.0029	2.5211%	0.0534	64.2578%	0.9244%
GPU72	2⁶⁴	1.1712	65.6250%	13000	220000	0.0030	1.4300%	1.1742	66.1165%	0.4915%
Difference	+4	+18.4411	+2.0221%	+2987000	+99780000	+1.0194	+6.6022%	+19.4606	+4.1292%	+4.1292%

Known prime factors (1 factor, 94.7 bits, 0.00311643% 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
3039163	32476447595790554476257720881	29	94.713	5342992066531238119880 2³ × 5 × 11 × 41 × 641 × 3719 × 8867 × 14011579	2017-08-04	8867	14011579	2.012e+9	0.0952	0.1760

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.806%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.147%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.249%
2010-10-08T05:57:00	markr	tiny	110000	2420000		-		-	-	0.029	-	-	2.657%
2016-10-10T15:03:06	Squeeky_Squirrel	P4_2600	195000	5313750	6	-		-	-	0.058	-	-	3.492%
2017-01-04T22:58:49	Jocelyn Larouche	low 4M	132000	132000		-		-	-	0.016	-	-	0.999%
2017-07-30T01:23:09	Jocelyn Larouche	low 4M	390000	3900000	6	-		-	-	0.072	-	-	3.584%
2017-08-05T00:20:56	mikr	MSI	3000000	100000000	12		32476447595790554476257720881	29	94.713	1.022	0.517	2.045	8.032%
2020-09-07T14:32:35	Jocelyn Larouche	Manual testing	425495	6078326	6	-		-	-	0.091	-	-	4.001%
2022-01-06T11:34:33	Jocelyn Larouche	Manual testing	1357832	116447100		-	skipped known factor: 32476447595790554476257720881	-	-	0.941	-	-	7.675%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-03-02T00:00:00	Jayson King	v4_computers	2⁶⁰	2⁶¹		-	-	0.051	-	-
2009-02-13T06:06:00	Sturle Sunde	goscha.ifi	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-10-22T00:43:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.323	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.646	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.229	-	-
2015-06-03T21:52:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.459	-	-
2021-02-21T11:36:42	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.459	-	-
2021-02-22T09:03:45	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.918	-	-
2017-05-05T02:55:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.918	-	-
2021-04-09T23:45:21	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.397 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.397 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.397

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-13T08:34:00	Martti Järvi	Wanda	50000	5000000						3	0.349
2011-06-14T14:35:00	Pool Party	desk_2	50000	5000000						3	0.349
2013-09-30T21:46:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-26T21:40:28	Bruce	Desk7	50000	5000000						3	0.349

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	curtisc	v4_computers	8CEC2E0B0EFB07D2	0.259

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:11:59

alpertron

Manual testing

32476447595790554476257720881

C11C49FA89A1E7__

2017-11-17T16:25:00

Oliver Kruse

Threadripper

32476447595790554476257720881

C11C49FA89A1E7__

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 = 1357832, B2 = 116447100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1357832 (P-1 stage 1)

B1 = 425495, B2 = 6078326 (P-1 stage 2)

B1 = 390000, B2 = 3900000 (P-1 stage 2)

B1 = 195000, B2 = 5313750 (P-1 stage 2)

B1 = 425495 (P-1 stage 1)

B1 = 390000 (P-1 stage 1)

B1 = 110000, B2 = 2420000 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 132000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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: 2022-01-06T11:34:33+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