M2674039 Mersenne number exponent details

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M2674039

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is 2 ^2674039 - 1

has 804966 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	1BC1B06B2AA46882	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	22.2902	67.6471%	629966	2519864	0.0821	3.3015%	22.3723	68.7152%	1.0681%
PrimeNet	2⁵⁹	0.0287	62.7119%	11000	200000	0.0024	2.7088%	0.0311	63.7219%	1.0101%
GPU72	2⁶³	0.5969	65.0794%	13000	220000	0.0027	1.6216%	0.5996	65.6456%	0.5663%
Difference	+5	+21.6933	+2.5677%	+616966	+2299864	+0.0794	+1.6799%	+21.7727	+3.0695%	+3.0695%

Known prime factors (1 factor, 71.2 bits, 0.00266309% 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
2674039	2734907274600489611369	22	71.212	511381336360556 2² × 59357 × 2153837527	2019-07-30	59357	2153837527	329.61	13.148	24.546

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	-	-	0.240%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.785%
2010-11-19T22:14:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-07T21:42:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.548%
2016-06-12T23:59:48	Jocelyn Larouche	Manual testing	151903	4567500	6	-		-	-	0.044	-	-	3.185%
2016-12-18T19:43:05	Jocelyn Larouche	low 4M	182283	182283		-		-	-	0.020	-	-	1.163%
2016-12-29T21:56:35	Jocelyn Larouche	low 4M	218739	218739		-		-	-	0.024	-	-	1.277%
2017-03-04T18:15:44	Jocelyn Larouche	low 4M	314983	3149830	6	-		-	-	0.053	-	-	3.267%
2018-08-29T01:29:34	Jocelyn Larouche	low 4M	629966	629966		-		-	-	0.071	-	-	2.071%
2018-08-30T21:10:17	Jocelyn Larouche	low 4M	629966	1259932		-		-	-	0.074	-	-	2.681%
2018-09-03T21:22:16	Jocelyn Larouche	low 4M	629966	1889898		-		-	-	0.078	-	-	3.043%
2018-09-04T10:43:03	Jocelyn Larouche	low 4M	629966	2519864		-		-	-	0.082	-	-	3.301%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:19	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-27T02:50:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-20T12:09:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.367	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.734	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.397	-	-
2016-01-25T14:29:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.795	-	-
2017-09-10T15:01:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.589	-	-
2019-04-22T13:11:28	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.413 GHz-days
Estimated T-Level:	1.650

Digits	B1	Curves	Complete	FacMiss
20	11000	33 / 100	0.330	71.773%
25	50000	33 / 280	0.118	88.864%

New Calculation Method

Total ECM effort:	3.413 GHz-days
Estimated T-Level:	1.650

Digits	B1	Complete	FacMiss
20	11000	1.065	34.489%
25	50000	0.096	90.827%
30	250000	0.006	99.409%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	3.103
50000	5000000	2734907274600489611369	3	0.310

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-11T06:48:00	willreid	jing	50000	5000000						3	0.310
2009-03-11T07:16:00	willreid	jing	50000	5000000						3	0.310
2012-12-10T18:54:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.310
2014-12-16T23:09:00	arnaud	srv-630	50000	5000000						3	0.310
2016-03-28T14:34:50	Jason U	Server7	50000	5000000						3	0.310
2016-04-17T04:38:32	Jason U	Server7	50000	5000000						3	0.310
2016-10-04T14:59:56	lettp	Home	50000	5000000						3	0.310
2017-07-06T12:37:11	Bruce	eleven	50000	5000000						3	0.310
2017-11-12T13:09:48	Roman O. Vorobiev	Home	50000	5000000						3	0.310
2018-06-02T08:33:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-07-30T12:27:40	Chang Chia-Tche	ex-ctcpc	50000	5000000	2734907274600489611369	71.212	3	2	5166600456949367	3	0.310

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	1BC1B06B2AA46882	0.207
2018-07-24T23:13:03	kkmrkkblmbrbk	old	1BC1B06B2AA46882	0.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-07-31T01:59:09

Niels_Mache_Nextcloud

SuperDry-X

2734907274600489611369

14FEF2B97FF9A540

2019-08-01T01:48:34

kkmrkkblmbrbk

c5.large

2734907274600489611369

14FEF2B97FF9A540

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 = 629966, B2 = 2519864 (P-1 stage 2)

B1 = 629966, B2 = 1889898 (P-1 stage 2)

B1 = 629966, B2 = 1259932 (P-1 stage 2)

B1 = 629966 (P-1 stage 1)

B1 = 314983, B2 = 3149830 (P-1 stage 2)

B1 = 151903, B2 = 4567500 (P-1 stage 2)

B1 = 314983 (P-1 stage 1)

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

B1 = 218739 (P-1 stage 1)

B1 = 182283 (P-1 stage 1)

B1 = 151903 (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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-08-01T01:48:34+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