M2681681 Mersenne number exponent details

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M2681681

<<<

>>>

is 2 ^2681681 - 1

has 807267 decimal digits

takes 0.207 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	E5E1107CBD1941C4	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	2⁶⁷	11.0803	67.1642%	2000000	60000000	0.5779	7.7023%	11.6582	69.6933%	2.5291%
PrimeNet	2⁵⁹	0.0286	62.7119%	12000	220000	0.0026	2.8395%	0.0312	63.7707%	1.0588%
GPU72	2⁶³	0.5952	65.0794%	13000	220000	0.0027	1.6225%	0.5979	65.6460%	0.5666%
Difference	+4	+10.4852	+2.0848%	+1987000	+59780000	+0.5752	+6.0798%	+11.0603	+4.0473%	+4.0473%

Known prime factors (1 factor, 81.7 bits, 0.00304616% 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
2681681	3896180362152846182854921	25	81.688	726443667638478660 2² × 3 × 5 × 13 × 109 × 307 × 27831875069	2018-06-09	307	27831875069	329,668	169.82	317.18

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.297%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.919%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.319%
2010-12-05T07:36:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.866%
2016-06-14T12:42:16	Jocelyn Larouche	Manual testing	151827	4567500	6	-		-	-	0.044	-	-	3.558%
2016-12-16T17:35:07	Jocelyn Larouche	low 4M	182192	182192		-		-	-	0.020	-	-	1.327%
2016-12-29T21:56:33	Jocelyn Larouche	low 4M	218630	218630		-		-	-	0.024	-	-	1.453%
2017-03-03T01:10:48	Jocelyn Larouche	low 4M	314827	3148270	6	-		-	-	0.053	-	-	3.632%
2018-02-20T11:48:59	Jocelyn Larouche	low 4M	377792	377792		-		-	-	0.042	-	-	1.873%
2019-07-04T12:48:23	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.578	-	-	7.702%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-26T06:53:00	Sturle Sunde	gaudi.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-14T21:23:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.366	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.732	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.393	-	-
2016-01-25T14:29:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.787	-	-
2017-09-13T08:55:32	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.573	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.001 GHz-days
Estimated T-Level:	1.450

Digits	B1	Curves	Complete	FacMiss
20	11000	29 / 100	0.290	74.717%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	3.001 GHz-days
Estimated T-Level:	1.450

Digits	B1	Complete	FacMiss
20	11000	0.935	39.240%
25	50000	0.085	91.893%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.794
50000	5000000	3896180362152846182854921	2	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-09T00:06:00	SubPrime	c2d0	50000	5000000						3	0.310
2010-07-31T19:38:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.310
2012-12-12T22:53:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.310
2014-12-29T04:56:00	arnaud	SPR05	50000	5000000						3	0.310
2016-01-29T10:05:45	Jason U	Server7	50000	5000000						3	0.310
2016-04-24T17:33:33	Marius Zens	KBWR_TV3	50000	5000000						3	0.310
2016-10-21T15:54:11	lettp	Home	50000	5000000						3	0.310
2017-07-08T12:46:38	Bruce	eleven	50000	5000000						3	0.310
2017-11-18T03:06:58	Angel Pescador		50000	5000000						3	0.310
2018-06-10T00:44:27	Chang Chia-Tche	ex-ctcpc	50000	5000000	3896180362152846182854921	81.688	2	2		2	0.207

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	E5E1107CBD1941C4	0.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-06-10T18:54:11

Luigi Morelli

Imac

3896180362152846182854921

3BA591584DED7D__

2018-06-11T02:50:36

Oliver Kruse

GTX-3

3896180362152846182854921

3BA591584DED7D__

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 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 314827, B2 = 3148270 (P-1 stage 2)

B1 = 151827, B2 = 4567500 (P-1 stage 2)

B1 = 377792 (P-1 stage 1)

B1 = 314827 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 218630 (P-1 stage 1)

B1 = 182192 (P-1 stage 1)

B1 = 151827 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-04T12:48:23+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