M3152167 Mersenne number exponent details

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M3152167

<<<

>>>

is 2 ^3152167 - 1

has 948897 decimal digits

takes 0.268 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	0FE061FEFAD834B8	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	37.8745	68.1159%	1222824	116447100	0.9257	6.9972%	38.8002	70.3469%	2.2310%
PrimeNet	2⁶⁰	0.0487	63.3333%	13000	240000	0.0031	2.6502%	0.0519	64.3051%	0.9717%
GPU72	2⁶⁴	1.1292	65.6250%	15000	240000	0.0034	1.5444%	1.1325	66.1559%	0.5309%
Difference	+5	+36.7453	+2.4909%	+1207824	+116207100	+0.9223	+5.4527%	+37.6676	+4.1910%	+4.1910%

Known prime factors (1 factor, 89.3 bits, 0.00283350% 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
3152167	770915387352048985727993959	27	89.317	122283398587709500437 3 × 2399 × 31277 × 563357 × 964289	2019-05-03	563357	964289	77,454,433	0.0722	0.1415

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	-	-	0.203%
2009-07-03T21:39:00	Carsten Kossendey	leela	15000	183750		-		-	-	0.003	-	-	0.657%
2011-09-07T12:13:00	Squeeky_Squirrel	T7500_2200	55000	948750		-		-	-	0.013	-	-	1.607%
2013-09-04T14:24:00	Squeeky_Squirrel	P4_2600	110000	2502500		-		-	-	0.030	-	-	2.393%
2015-11-24T14:15:18	HBendtz	Manual testing	500000	12000000	12	-		-	-	0.139	-	-	4.269%
2019-05-03T15:23:20	mikr	MSI	3000000	12000000			770915387352048985727993959	27	89.317	0.370	0.537	0.740	4.958%
2021-01-16T17:21:45	Jocelyn Larouche	Manual testing	315216	3152167	6	-		-	-	0.058	-	-	3.003%
2022-01-06T11:35:07	Jocelyn Larouche	Manual testing	1222824	116447100		-	skipped known factor: 770915387352048985727993959	-	-	0.926	-	-	6.997%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-10T12:33:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-04T19:43:00	markr	Manual testing	2¹	2⁶²		-	-	0.195	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.311	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.623	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.185	-	-
2015-06-17T09:59:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.371	-	-
2017-04-22T18:10:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.741	-	-
2019-02-04T14:28:18	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.483	-	-
2021-01-08T11:34:53	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.97	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.757 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:	1.757 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	1.757

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-02T06:49:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.351
2011-08-06T17:23:00	Andrew B	dell_xps_8100_i7_x86	50000	5000000						3	0.351
2014-02-26T12:22:00	S00030	op9020-usff	50000	5000000						3	0.351
2016-06-18T16:30:25	WileECoyote	RoadRunner	50000	5000000						3	0.351
2018-02-22T17:16:37	alpertron	laptop2	50000	5000000						3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-19T00:00:00	ANONYMOUS	v4_computers	0FE061FEFAD834B8	0.268
1999-06-06T00:00:00	ANONYMOUS	v4_computers	0FE061FEFAD834B8	0.268

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-05-04T13:00:56

artorollo

fourth

770915387352048985727993959

D1AECFDD97DAD03A

2019-05-05T04:48:15

kkmrkkblmbrbk

c5.large

770915387352048985727993959

D1AECFDD97DAD03A

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 = 1222824, B2 = 116447100 (P-1 stage 2)

B1 = 3000000, B2 = 12000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1222824 (P-1 stage 1)

B1 = 500000, B2 = 12000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 315216, B2 = 3152167 (P-1 stage 2)

B1 = 315216 (P-1 stage 1)

B1 = 110000, B2 = 2502500 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 55000, B2 = 948750 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 183750 (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

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-06T11:35:07+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