M2737489 Mersenne number exponent details

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M2737489

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>>>

is 2 ^2737489 - 1

has 824067 decimal digits

takes 0.211 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	9AADCF8D2CCA5EE6	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	21.7736	67.6471%	2700000	84000000	0.7984	7.6731%	22.5720	70.1295%	2.4825%
PrimeNet	2⁵⁹	0.0281	62.7119%	12000	220000	0.0026	2.8501%	0.0307	63.7746%	1.0628%
GPU72	2⁶³	0.5830	65.0794%	14000	240000	0.0029	1.7076%	0.5860	65.6757%	0.5963%
Difference	+5	+21.1905	+2.5677%	+2686000	+83760000	+0.7955	+5.9656%	+21.9860	+4.4539%	+4.4539%

Known prime factors (1 factor, 73.4 bits, 0.00268188% 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
2737489	12603230514468410841151	23	73.416	2301969161240175 3 × 5² × 7 × 31 × 141442037557	2020-08-05	31	141442037557	809.94	863.03	1,611.9

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%
2010-12-19T21:43:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.269%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.372%
2011-01-20T22:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.539%
2011-04-27T08:29:00	James Heinrich	WHS	185000	4625000		-		-	-	0.048	-	-	3.314%
2016-10-24T16:45:58	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.673%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:20	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.056	-	-
2009-01-28T01:30:00	Sturle Sunde	papageno.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-09T08:28:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.112	-	-
2013-01-14T12:27:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.359	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.717	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.365	-	-
2016-02-03T11:43:35	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.730	-	-
2017-10-05T11:09:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.460	-	-
2019-02-15T01:31:28	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.92	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.529 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	3.529 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.097	33.395%
25	50000	0.099	90.563%
30	250000	0.006	99.391%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.426
50000	5000000	12603230514468410841151	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-21T12:07:00	Smurgs	23-3-09	50000	5000000						3	0.311
2010-09-01T19:01:00	Lupo	yorick	50000	5000000						3	0.311
2013-02-21T15:49:00	Xyzzy	J	50000	5000000						3	0.311
2015-02-28T02:35:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-12T18:27:09	Tapio Pätilä	JULIUS	50000	5000000						3	0.311
2016-05-09T09:06:51	lettp	Home	50000	5000000						3	0.311
2016-12-20T18:54:34	Ensigma	vps_sing	50000	5000000						3	0.311
2017-08-17T00:54:37	Bruce	eleven	50000	5000000						3	0.311
2017-12-16T10:37:14	Conductor	Andrew	50000	5000000						3	0.311
2018-08-28T00:32:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2020-07-29T11:56:09	GAN	LMS-08	50000	5000000						3	0.311
2020-08-05T21:32:34	GAN	LMS-15	50000	5000000	12603230514468410841151	73.416	1	2	1456418356929361	1	0.104

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	9AADCF8D2CCA5EE6	0.211
2018-08-10T16:36:54	kkmrkkblmbrbk	old	9AADCF8D2CCA5EE6	0.211

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-09T05:11:30

fre_games

gpu

12603230514468410841151

9A1BFC570DE8A6C5

2020-08-09T20:33:09

kutens

sol

12603230514468410841151

9A1BFC570DE8A6C5

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 = 185000, B2 = 4625000 (P-1 stage 2)

B1 = 185000 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-09T20:33:09+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