M2747671 Mersenne number exponent details

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M2747671

<<<

>>>

is 2 ^2747671 - 1

has 827132 decimal digits

takes 0.212 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	9151BC4EA1466E13	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	21.6929	67.6471%	2700000	84000000	0.7984	7.6760%	22.4913	70.1305%	2.4834%
PrimeNet	2⁵⁹	0.0279	62.7119%	12000	220000	0.0026	2.8520%	0.0306	63.7753%	1.0635%
GPU72	2⁶³	0.5809	65.0794%	14000	240000	0.0029	1.7088%	0.5838	65.6761%	0.5967%
Difference	+5	+21.1120	+2.5677%	+2686000	+83760000	+0.7955	+5.9672%	+21.9075	+4.4544%	+4.4544%

Known prime factors (2 factors, 144.9 bits, 0.00527243% 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
2747671	186355274432270624111	21	67.337	33911497124705 5 × 3041 × 2230285901	2022-05-06	3041	2230285901	19.444	13.609	25.417
2747671	218567813918929424298287	24	77.532	39773286888956033 7 × 27437 × 207088899187	2017-01-01	27437	207088899187	12,136	1,263.6	2,360.0

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
2747671	186355274432270624111 218567813918929424298287	40731264944923551985082066614020449718197857	44	144.869

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.241%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.798%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.269%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.373%
2011-01-21T23:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.539%
2011-05-02T22:53:00	James Heinrich	WHS	190000	4655000		-		-	-	0.049	-	-	3.334%
2016-11-26T17:34:22	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.676%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:20	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-27T05:19:00	Sturle Sunde	interavia.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-06T10:28:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.112	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.357	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.715	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.360	-	-
2016-02-04T08:53:27	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.720	-	-
2022-05-07T08:27:36	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	5.439	-	-
2022-05-06T08:35:25	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	186355274432270624111	67.337	21	8.630	0.431	17.54
2022-05-07T08:27:36	LordJulius	Manual testing	2⁶⁷	2⁶⁸	186355274432270624111	67.337	21	8.630	0.431	17.54

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.181 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	2.181 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.870
50000	5000000	218567813918929424298287	3	0.312

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-18T08:38:00	Marzbug	Xeon	50000	5000000						3	0.312
2010-09-06T06:34:00	James Hintz	ryan	50000	5000000						3	0.312
2013-02-27T17:37:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-07T12:09:00	Jason U	Server7	50000	5000000						3	0.312
2016-02-12T16:34:20	Jason U	Server7	50000	5000000						3	0.312
2016-05-12T10:10:47	lettp	Home	50000	5000000						3	0.312
2017-01-01T15:52:05	Bruce	eleven	50000	5000000	218567813918929424298287	77.532	3	2		3	0.312

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-26T00:00:00	ANONYMOUS	v4_computers	9151BC4EA1466E13	0.212
1999-11-24T00:00:00	Charlie Dorian	v4_computers	9151BC4EA1466E13	0.212

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20T12:15:46

Oliver Kruse

GTX-0

218567813918929424298287

DA3550BE6838D8__

2017-12-05T16:29:03

kkmrkkblmbrbk

c4.xlarge

218567813918929424298287

DA3550BE6838D8__

2022-05-09T02:51:29

aperson1

2012_VP113

186355274432270624111

218567813918929424298287

DA3550BE6838D8D6

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 190000, B2 = 4655000 (P-1 stage 2)

B1 = 190000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

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

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: 2022-05-09T02:51:29+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