M3147721 Mersenne number exponent details

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M3147721

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is 2 ^3147721 - 1

has 947559 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	25963A2B86FBA42A	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	37.9280	68.1159%	3147721	668661840	4.8632	9.7228%	42.7912	71.2160%	3.1000%
PrimeNet	2⁶⁰	0.0488	63.3333%	13000	240000	0.0031	2.6495%	0.0519	64.3048%	0.9715%
GPU72	2⁶⁴	1.1308	65.6250%	15000	240000	0.0034	1.5440%	1.1341	66.1558%	0.5308%
Difference	+5	+36.7972	+2.4909%	+3132721	+668421840	+4.8599	+8.1788%	+41.6571	+5.0602%	+5.0602%

Known prime factors (1 factor, 89.6 bits, 0.00284744% 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
3147721	957618334098749669700173377	27	89.630	152112962695669290528 2⁵ × 3 × 32203 × 637573 × 77173597	2019-04-06	637573	77173597	51,623,012	0.5933	0.9692

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%
2009-07-03T07:24:00	Carsten Kossendey	leela	15000	183750		-		-	-	0.003	-	-	0.657%
2011-09-06T18:30:00	Squeeky_Squirrel	T7500_2200	55000	935000		-		-	-	0.013	-	-	1.600%
2013-09-02T09:04:00	Squeeky_Squirrel	P4_2600	110000	2475000		-		-	-	0.029	-	-	2.387%
2016-11-15T10:24:24	Squeeky_Squirrel	P4_2600	195000	5460000	12	-		-	-	0.059	-	-	3.166%
2018-07-12T10:20:23	Jocelyn Larouche	low 4M	636000	6360000	12	-		-	-	0.117	-	-	3.836%
2019-04-06T03:20:20	mikr	MSI	3000000	100000000	12		957618334098749669700173377	27	89.630	1.022	0.536	2.045	7.430%
2021-11-20T20:53:50	Jocelyn Larouche	Manual testing	3147721	3147721		-		-	-	0.388	-	-	3.426%
2021-12-09T14:58:54	Jocelyn Larouche	Manual testing	3147721	31477210	12	-		-	-	0.579	-	-	6.092%
2021-12-21T19:29:56	Jocelyn Larouche	Manual testing	3147721	140228550		-	skipped known factor: 957618334098749669700173377	-	-	1.310	-	-	7.859%
2021-12-22T09:19:53	Jocelyn Larouche	Manual testing	3147721	668661840		-	skipped known factor: 957618334098749669700173377	-	-	4.863	-	-	9.723%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-12T05:17:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-04T02:10:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-07T14:05:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.312	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.624	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.187	-	-
2015-06-17T09:59:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.374	-	-
2021-01-03T13:46:16	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.374	-	-
2017-04-20T01:22:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.748	-	-
2018-12-24T09:14:09	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.496	-	-
2022-01-09T02:58:42	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	18.99	-	-

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
2009-07-08T13:38:00	Gerry Snyder	blu	50000	5000000						3	0.351
2011-08-03T14:20:00	Andrew B	dell_xps_8100_i7_x86	50000	5000000						3	0.351
2014-02-20T20:09:00	arnaud	Chamot18	50000	5000000						3	0.351
2016-06-20T01:06:01	LazyDude	Buyer03	50000	5000000						3	0.351
2018-02-12T16:06:18	tanaydin	iMac	50000	5000000						3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	25963A2B86FBA42A	0.268

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-04-06T04:38:39

ATH

ec2-PRPCF

957618334098749669700173377

98C8649EE7D335AD

2019-04-07T00:36:27

oodaira

com1

957618334098749669700173377

98C8649EE7D335AD

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 = 3147721, B2 = 668661840 (P-1 stage 2)

B1 = 3147721, B2 = 140228550 (P-1 stage 2)

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

B1 = 3147721, B2 = 31477210 (P-1 stage 2)

B1 = 3147721 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 636000, B2 = 6360000 (P-1 stage 2)

B1 = 636000 (P-1 stage 1)

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

B1 = 110000, B2 = 2475000 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 55000, B2 = 935000 (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

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