M2647321 Mersenne number exponent details

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M2647321

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>>>

is 2 ^2647321 - 1

has 796924 decimal digits

takes 0.204 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	F37AC8B54738F409	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	22.5152	67.6471%	2000000	50000000	0.5169	6.8572%	23.0320	69.8656%	2.2185%
PrimeNet	2⁵⁹	0.0290	62.7119%	11000	200000	0.0024	2.7038%	0.0314	63.7201%	1.0082%
GPU72	2⁶³	0.6029	65.0794%	13000	200000	0.0026	1.5744%	0.6055	65.6292%	0.5498%
Difference	+5	+21.9123	+2.5677%	+1987000	+49800000	+0.5143	+5.2828%	+22.4266	+4.2364%	+4.2364%

Known prime factors (1 factor, 71.3 bits, 0.00269337% 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
2647321	2911139834869305856871	22	71.302	549827511448235 5 × 263 × 418119780569	2020-07-14	263	418119780569	226.54	2,551.2	4,765.0

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2009-06-22T11:40:00	harlee	P4_2600	30000	420000		-		-	-	0.006	-	-	1.207%
2011-01-20T12:24:00	James Heinrich	i7-920	180000	4275000		-		-	-	0.045	-	-	3.228%
2016-12-28T03:20:12	Jocelyn Larouche	low 4M	171988	171988		-		-	-	0.019	-	-	1.126%
2016-12-29T21:56:29	Jocelyn Larouche	low 4M	206385	206385		-		-	-	0.023	-	-	1.238%
2017-05-08T05:55:49	Jocelyn Larouche	low 4M	360000	3600000	6	-		-	-	0.060	-	-	3.422%
2019-11-28T16:16:15	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.857%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	foxkid	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:18	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-30T15:09:00	Sturle Sunde	golan.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-06-11T04:53:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.116	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.371	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.742	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.411	-	-
2016-01-21T23:03:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.823	-	-
2017-09-08T08:21:16	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.646	-	-
2019-02-18T10:31:25	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.29	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.614 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	3.614 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.129	32.335%
25	50000	0.102	90.299%
30	250000	0.006	99.374%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.408
50000	5000000	2911139834869305856871	2	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-27T19:45:00	S530729	AMD-X5200	50000	5000000						3	0.310
2010-07-16T16:48:00	James Classen	towerofart	50000	5000000						3	0.310
2012-11-30T00:31:00	Donna Noble	PH2x6	50000	5000000						3	0.310
2014-11-05T05:10:00	arnaud	srv-630	50000	5000000						3	0.310
2016-01-24T08:14:16	S36049	Wolle4	50000	5000000						3	0.310
2016-04-06T19:39:39	Jason U	Server7	50000	5000000						3	0.310
2016-09-16T14:30:42	Hinesp	C742F5B97	50000	5000000						3	0.310
2017-06-30T18:07:56	Sebastian Hornbostel	V2	50000	5000000						3	0.310
2017-11-01T08:54:51	Sebastian Hornbostel	V2	50000	5000000						3	0.310
2018-05-08T16:16:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-07-12T14:49:01	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-14T09:09:35	GAN	LMS-06	50000	5000000	2911139834869305856871	71.302	2	2	91852686575996	2	0.207

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	foxkid	v4_computers	F37AC8B54738F409	0.204
2018-07-16T14:16:49	kkmrkkblmbrbk	old	F37AC8B54738F409	0.204

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-16T23:37:03

Klaus Nordmann

no1

2911139834869305856871

813A227C610BE3AF

2020-07-17T01:03:07

oodaira

com2

2911139834869305856871

813A227C610BE3AF

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 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 360000, B2 = 3600000 (P-1 stage 2)

B1 = 180000, B2 = 4275000 (P-1 stage 2)

B1 = 360000 (P-1 stage 1)

B1 = 206385 (P-1 stage 1)

B1 = 180000 (P-1 stage 1)

B1 = 171988 (P-1 stage 1)

B1 = 30000, B2 = 420000 (P-1 stage 2)

B1 = 30000 (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

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-17T01:03:07+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