M2756797 Mersenne number exponent details

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M2756797

<<<

>>>

is 2 ^2756797 - 1

has 829879 decimal digits

takes 0.213 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	BA2C9F9E847EF948	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	21.6211	67.6471%	2700000	84000000	0.7984	7.6786%	22.4195	70.1313%	2.4842%
PrimeNet	2⁵⁹	0.0279	62.7119%	12000	220000	0.0026	2.8538%	0.0305	63.7760%	1.0641%
GPU72	2⁶³	0.5789	65.0794%	15000	240000	0.0031	1.7447%	0.5820	65.6886%	0.6092%
Difference	+5	+21.0421	+2.5677%	+2685000	+83760000	+0.7954	+5.9339%	+21.8375	+4.4427%	+4.4427%

Known prime factors (1 factor, 76.0 bits, 0.00275652% 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
2756797	75115699912032977544559	23	75.992	13623727084735107 3 × 17 × 83833 × 3186476729	2020-08-03	83833	3186476729	4,414.0	19.452	36.314

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	-	-	0.242%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.799%
2010-12-21T11:04:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.270%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.373%
2011-01-23T12:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.539%
2011-05-07T14:06:00	James Heinrich	WHS	190000	4655000		-		-	-	0.049	-	-	3.336%
2016-12-27T08:05:15	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.679%
2017-01-10T10:25:14	Jocelyn Larouche	low 4M	228000	228000		-		-	-	0.026	-	-	1.311%

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	-	-
2009-02-13T21:37:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-27T07:26:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.356	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.712	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.355	-	-
2016-02-05T15:45:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.711	-	-
2017-10-09T09:26:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.421	-	-
2019-02-20T01:17:43	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.222 GHz-days
Estimated T-Level:	1.550

Digits	B1	Curves	Complete	FacMiss
20	11000	31 / 100	0.310	73.230%
25	50000	31 / 280	0.111	89.502%

New Calculation Method

Total ECM effort:	3.222 GHz-days
Estimated T-Level:	1.550

Digits	B1	Complete	FacMiss
20	11000	1.000	36.788%
25	50000	0.090	91.358%
30	250000	0.006	99.445%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	3.118
50000	5000000	75115699912032977544559	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-14T22:05:00	Martti Järvi	Mardeni	50000	5000000						3	0.312
2010-09-12T17:28:00	James Hintz	ryan	50000	5000000						3	0.312
2013-03-02T10:24:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-10T14:48:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-14T02:13:15	Bruce	Desk8	50000	5000000						3	0.312
2016-05-15T08:43:58	Jason U	Server7	50000	5000000						3	0.312
2017-01-10T19:55:38	enderhirodantezeus	alien	50000	5000000						3	0.312
2017-08-01T10:24:02	Lelikoid	QH	50000	5000000						3	0.312
2017-12-26T11:33:23	Sebastian Hornbostel	V2	50000	5000000						3	0.312
2018-09-29T01:57:35	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-03T13:32:54	GAN	LMS-16	50000	5000000	75115699912032977544559	75.992	1	2	5728836509154276	1	0.104

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-04T00:00:00	ANONYMOUS	v4_computers	BA2C9F9E847EF948	0.213
2018-08-15T22:51:21	kkmrkkblmbrbk	old	BA2C9F9E847EF948	0.213

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-07T01:36:46

fre_games

gpu

75115699912032977544559

21F7B366D88F6EAD

2020-08-07T19:20:19

marssystems

SYSTEM01

75115699912032977544559

21F7B366D88F6EAD

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 = 228000 (P-1 stage 1)

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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-07T19:20:19+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