M3171671 Mersenne number exponent details

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M3171671

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>>>

is 2 ^3171671 - 1

has 954769 decimal digits

takes 0.270 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	-unknown-	-unknown-
PRP	1395659672630008	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	18.7929	67.6471%	1000000	134343300	1.0200	7.6231%	19.8129	70.1134%	2.4663%
PrimeNet	2⁶⁰	0.0484	63.3333%	13000	240000	0.0031	2.6532%	0.0516	64.3062%	0.9728%
GPU72	2⁶⁴	1.1222	65.6250%	15000	260000	0.0035	1.5821%	1.1257	66.1688%	0.5438%
Difference	+4	+17.6707	+2.0221%	+985000	+134083300	+1.0165	+6.0410%	+18.6872	+3.9445%	+3.9445%

Known prime factors (1 factor, 76.2 bits, 0.00240321% 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
3171671	88129190547342319467793	23	76.222	13893179738273976 2³ × 3 × 7 × 97 × 367 × 2323028693	2021-07-10	367	2323028693	5,614.8	15.620	29.173

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.252%
2009-07-03T00:49:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.781%
2011-09-10T18:45:00	Squeeky_Squirrel	T7500_2200	60000	960000		-		-	-	0.013	-	-	1.876%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	80237	80237		-		-	-	0.010	-	-	0.753%
2014-09-25T21:11:00	Jocelyn Larouche	Manual testing	100474	100474		-		-	-	0.012	-	-	0.862%
2015-09-25T14:29:03	Squeeky_Squirrel	P4_2600	145000	3625000		-		-	-	0.041	-	-	3.079%
2016-04-22T05:24:19	Jocelyn Larouche	Manual testing	384000	11584623	6	-		-	-	0.123	-	-	4.529%
2019-01-05T23:03:04	King	FactorFinder	2131475	59681306	6	-		-	-	0.650	-	-	7.235%
2022-02-22T08:55:09	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.623%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-08T17:58:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-27T06:54:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.097	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.310	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.619	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.178	-	-
2015-06-17T10:00:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.356	-	-
2017-04-25T10:21:53	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.712	-	-
2019-01-14T11:03:51	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.424	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.154 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	7.154 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	6.685
50000	5000000	88129190547342319467793	4	0.469

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-25T17:26:00	abc	C30D35CA5	50000	5000000						3	0.352
2011-08-12T09:16:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.352
2014-03-26T14:39:00	arnaud	Chamot18	50000	5000000						3	0.352
2016-08-31T21:24:37	bayanne	iMac	50000	5000000						3	0.352
2018-03-17T16:12:44	Aare Vesi	h1	50000	5000000						3	0.352
2020-12-02T01:22:42	IanGlencross	glenx24	50000	5000000						7	0.821
2021-01-04T09:29:31	daveward2005	Dave2	50000	5000000						7	0.821
2021-02-03T11:50:57	Zenzoma	AM3700X_1	50000	5000000						7	0.821
2021-03-04T13:27:20	Zenzoma	AMD3970X	50000	5000000						7	0.821
2021-04-09T22:11:51	Zenzoma	AMD3970X	50000	5000000						7	0.821
2021-06-05T15:10:10	daveward2005	d12436	50000	5000000						7	0.821
2021-07-10T17:01:46	daveward2005	d12436	50000	5000000	88129190547342319467793	76.222	4	2	7692236685495577	4	0.469

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-30T00:00:00	ANONYMOUS	v4_computers	7325FA348F14DA__	0.270

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-11T05:03:24

SRJ2877

LTOS

88129190547342319467793

1395659672630008

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 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 2131475, B2 = 59681306 (P-1 stage 2)

B1 = 2131475 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 384000, B2 = 11584623 (P-1 stage 2)

B1 = 384000 (P-1 stage 1)

B1 = 145000, B2 = 3625000 (P-1 stage 2)

B1 = 145000 (P-1 stage 1)

B1 = 60000, B2 = 960000 (P-1 stage 2)

B1 = 100474 (P-1 stage 1)

B1 = 80237 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-22T08:55:09+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