M2665499 Mersenne number exponent details

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M2665499

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is 2 ^2665499 - 1

has 802396 decimal digits

takes 0.206 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	7A9EC01EE5DAEFF5	double-checked
PRP	30FB601D5F7B962F	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	22.3616	67.6471%	2000000	50000000	0.5169	6.8621%	22.8785	69.8672%	2.2201%
PrimeNet	2⁵⁹	0.0288	62.7119%	11000	200000	0.0024	2.7073%	0.0312	63.7213%	1.0095%
GPU72	2⁶³	0.5988	65.0794%	13000	220000	0.0027	1.6206%	0.6015	65.6453%	0.5659%
Difference	+5	+21.7629	+2.5677%	+1987000	+49780000	+0.5141	+5.2416%	+22.2770	+4.2219%	+4.2219%

Known prime factors (1 factor, 95.9 bits, 0.00359797% 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
2665499	74121513856352541039587005049	29	95.904	13903872006020737775476 2² × 13² × 31 × 1979 × 335259873788849	2020-08-18	1979	335259873788849	5.405e+9	2,045,639	3,820,685

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	-	-	0.239%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	213750		-		-	-	0.003	-	-	0.780%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.370%
2011-02-03T14:32:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.547%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	129080	129080		-		-	-	0.014	-	-	0.964%
2016-06-08T10:37:13	Jocelyn Larouche	Manual testing	151988	4567500	6	-		-	-	0.044	-	-	3.184%
2016-12-18T19:43:07	Jocelyn Larouche	low 4M	182385	182385		-		-	-	0.020	-	-	1.163%
2017-01-10T10:25:00	Jocelyn Larouche	low 4M	218862	218862		-		-	-	0.025	-	-	1.277%
2017-03-07T20:00:33	Jocelyn Larouche	low 4M	315160	3151600	6	-		-	-	0.053	-	-	3.266%
2018-08-29T01:29:37	Jocelyn Larouche	low 4M	626630	626630		-		-	-	0.070	-	-	2.065%
2018-08-30T21:10:20	Jocelyn Larouche	low 4M	630320	630320		-		-	-	0.071	-	-	2.070%
2018-09-03T21:22:18	Jocelyn Larouche	low 4M	630320	1260640		-		-	-	0.074	-	-	2.680%
2018-09-04T10:43:06	Jocelyn Larouche	low 4M	630320	1890960		-		-	-	0.078	-	-	3.042%
2018-09-07T21:01:40	Jocelyn Larouche	low 4M	630320	2521280		-		-	-	0.082	-	-	3.301%
2019-11-22T14:04:09	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.862%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-13T00:00:00	JG12	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:18	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-30T17:41:00	Sturle Sunde	golli.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-05-20T14:06:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.368	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.737	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.402	-	-
2016-01-25T14:29:34	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.804	-	-
2017-09-08T08:21:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.607	-	-
2019-04-29T13:20:18	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.21	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.755 GHz-days
Estimated T-Level:	2.300

Digits	B1	Curves	Complete	FacMiss
20	11000	46 / 100	0.460	62.982%
25	50000	46 / 280	0.164	84.825%

New Calculation Method

Total ECM effort:	4.755 GHz-days
Estimated T-Level:	2.300

Digits	B1	Complete	FacMiss
20	11000	1.484	22.676%
25	50000	0.134	87.449%
30	250000	0.008	99.178%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.652
50000	5000000	74121513856352541039587005049	1	0.103

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-05T07:50:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.310
2010-07-17T12:47:00	ANONYMOUS		50000	5000000						3	0.310
2012-12-06T07:49:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.310
2014-12-06T21:09:00	arnaud	srv-630	50000	5000000						3	0.310
2016-01-25T12:43:28	Jason U	Server7	50000	5000000						3	0.310
2016-04-14T02:15:20	Jason U	Server7	50000	5000000						3	0.310
2016-09-25T08:37:07	lettp	Home	50000	5000000						3	0.310
2017-07-03T17:29:03	Bruce	eleven	50000	5000000						3	0.310
2017-11-07T11:51:35	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2018-05-24T18:07:14	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-06-27T11:33:24	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-18T13:24:32	GAN	LMS-12	50000	5000000						3	0.310
2020-07-24T18:09:19	GAN	LMS-03	50000	5000000						3	0.310
2020-07-31T20:39:02	GAN	LMS-12	50000	5000000						3	0.310
2020-08-08T14:39:09	GAN	LMS-13	50000	5000000						3	0.310
2020-08-18T10:08:08	GAN	KA-HP	50000	5000000	74121513856352541039587005049	95.904	1	2	3709440009392587	1	0.103

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-09T00:00:00	JG12	v4_computers	7A9EC01EE5DAEFF5	0.206
1997-12-13T00:00:00	JG12	v4_computers	7A9EC01EE5DAEFF5	0.206
1999-04-23T00:00:00	ANONYMOUS	v4_computers	7A9EC01EE5DAEFF5	0.206
2018-07-23T04:05:08	kkmrkkblmbrbk	old	7A9EC01EE5DAEFF5	0.206

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-18T15:21:04

CrypticClue

cruncher

74121513856352541039587005049

30FB601D5F7B962F

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 = 630320, B2 = 2521280 (P-1 stage 2)

B1 = 630320, B2 = 1890960 (P-1 stage 2)

B1 = 630320, B2 = 1260640 (P-1 stage 2)

B1 = 630320 (P-1 stage 1)

B1 = 626630 (P-1 stage 1)

B1 = 315160, B2 = 3151600 (P-1 stage 2)

B1 = 151988, B2 = 4567500 (P-1 stage 2)

B1 = 315160 (P-1 stage 1)

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

B1 = 218862 (P-1 stage 1)

B1 = 182385 (P-1 stage 1)

B1 = 151988 (P-1 stage 1)

B1 = 129080 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 213750 (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

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-18T15:21:04+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