M2095399 Mersenne number exponent details

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M2095399

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>>>

is 2 ^2095399 - 1

has 630778 decimal digits

takes 0.138 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	841BA0F991324A14	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	14.1806	68.6567%	2500000	125000000	0.8746	8.5641%	15.0552	71.3410%	2.6843%
PrimeNet	2⁵⁸	0.0183	63.7931%	9000	160000	0.0016	2.6767%	0.0200	64.7622%	0.9691%
GPU72	2⁶²	0.2932	66.1290%	9000	140000	0.0015	1.4010%	0.2947	66.6036%	0.4745%
Difference	+5	+13.8874	+2.5277%	+2491000	+124860000	+0.8731	+7.1630%	+14.7605	+4.7374%	+4.7374%

Known prime factors (1 factor, 85.6 bits, 0.00408331% 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
2095399	57094271819210356870451057	26	85.562	13623723171388923272 2³ × 31 × 11057 × 547831 × 9069017	2017-05-26	547831	9069017	6,533,595	0.0965	0.1063

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-07-27T07:14:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.020%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.415%
2011-01-09T14:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.596%
2011-01-22T12:29:00	James Heinrich	Q6600	140000	3150000		-		-	-	0.029	-	-	3.129%
2016-07-28T10:34:57	Jocelyn Larouche	Manual testing	186340	6300000	12	-		-	-	0.050	-	-	3.800%
2016-11-05T16:28:43	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.410%
2016-11-10T03:36:31	Jocelyn Larouche	low 4M	268329	268329		-		-	-	0.026	-	-	1.540%
2017-05-26T10:23:03	mikr	MSI	2500000	125000000	12		57094271819210356870451057	26	85.562	0.875	0.276	1.749	8.564%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T00:59:00	Sturle Sunde	nardi.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-24T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.147	-	-
2013-09-04T10:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.468	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.937	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.783	-	-
2015-10-31T16:44:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.566	-	-
2016-09-22T02:15:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.133	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.552 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	2.552 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	0.968	37.994%
25	50000	0.087	91.625%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.552

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-07T18:05:00	Martti Järvi	SKYNET	50000	5000000						3	0.255
2009-11-07T03:14:00	James Hintz	ryan	50000	5000000						3	0.255
2011-06-09T17:06:00	Beat Bucheli	I7	50000	5000000						3	0.255
2013-03-28T03:50:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-10-03T11:03:00	OS1	L3	50000	5000000						3	0.255
2015-07-29T19:14:00	guru	w1	50000	5000000						3	0.255
2016-02-20T19:08:26	arnaud	CHAMOT09	50000	5000000						3	0.255
2016-05-24T19:47:06	Jason U	Server7	50000	5000000						3	0.255
2016-08-12T13:45:50	Bruce	test	50000	5000000						3	0.255
2017-01-23T20:43:48	Bruce	Desk6	50000	5000000						3	0.255

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	841BA0F991324A14	0.138

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T22:58:37

Oliver Kruse

GTX-0

57094271819210356870451057

B5D9DCA194A99F__

2017-11-17T00:23:15

kkmrkkblmbrbk

c4.xlarge

57094271819210356870451057

B5D9DCA194A99F__

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 186340, B2 = 6300000 (P-1 stage 2)

B1 = 140000, B2 = 3150000 (P-1 stage 2)

B1 = 268329 (P-1 stage 1)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (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

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-11-17T00:23:15+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