M2090441 Mersenne number exponent details

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M2090441

<<<

>>>

is 2 ^2090441 - 1

has 629286 decimal digits

takes 0.137 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	9FF67241DA6D22BE	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	14.2142	68.6567%	2500000	125000000	0.8746	8.5621%	15.0888	71.3404%	2.6836%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6755%	0.0200	64.7618%	0.9687%
GPU72	2⁶²	0.2939	66.1290%	9000	140000	0.0015	1.4003%	0.2954	66.6033%	0.4743%
Difference	+5	+13.9203	+2.5277%	+2491000	+124860000	+0.8731	+7.1617%	+14.7934	+4.7370%	+4.7370%

Known prime factors (1 factor, 91.8 bits, 0.00439243% 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
2090441	4374446478977598181490855431	28	91.821	1046297522622642347115 3⁴ × 5 × 107 × 1699 × 3406709 × 4171459	2018-05-28	3406709	4171459	246,905,280	0.3288	0.6610

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	-	-	0.276%
2009-07-27T00:25:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.019%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.414%
2011-01-08T14:34:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.595%
2011-01-18T23:17:00	James Heinrich	Q6600	140000	3150000		-		-	-	0.029	-	-	3.128%
2016-07-24T21:21:51	Jocelyn Larouche	Manual testing	186340	6300000	12	-		-	-	0.050	-	-	3.799%
2016-11-05T03:54:49	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.410%
2016-11-08T17:01:23	Jocelyn Larouche	low 4M	268329	268329		-		-	-	0.026	-	-	1.540%
2017-05-07T10:15:52	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.562%

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	-	-
2009-01-02T23:36:00	Sturle Sunde	korsmo.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-20T09:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.147	-	-
2013-09-03T09:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.470	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.939	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.787	-	-
2015-11-06T09:16:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.575	-	-
2016-09-22T02:15:56	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.149	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.147 GHz-days
Estimated T-Level:	1.850

Digits	B1	Curves	Complete	FacMiss
20	11000	37 / 100	0.370	68.945%
25	50000	37 / 280	0.132	87.601%

New Calculation Method

Total ECM effort:	3.147 GHz-days
Estimated T-Level:	1.850

Digits	B1	Complete	FacMiss
20	11000	1.194	30.314%
25	50000	0.108	89.774%
30	250000	0.007	99.338%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	3.062
50000	5000000	4374446478977598181490855431	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-06T03:01:00	S36049	Wolle3	50000	5000000						3	0.255
2009-11-05T20:20:00	SubPrime	abd0	50000	5000000						3	0.255
2011-06-07T06:19:00	Eric Christenson	CA_Robotics_Bld_2	50000	5000000						3	0.255
2013-03-23T20:19:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-09-18T12:35:00	OS1	L3	50000	5000000						3	0.255
2015-07-28T01:09:00	guru	w6	50000	5000000						3	0.255
2016-04-23T06:24:29	Jason U	Server7	50000	5000000						3	0.255
2016-05-22T13:06:48	Bruce	Desk6	50000	5000000						3	0.255
2016-08-10T20:11:24	Bruce	test	50000	5000000						3	0.255
2017-01-18T12:52:45	Bruce	Desk6	50000	5000000						3	0.255
2017-08-06T12:52:44	Bruce	Desk6	50000	5000000						3	0.255
2017-12-28T05:53:14	Bruce	Desk6	50000	5000000						3	0.255
2018-05-28T01:52:51	Bruce	Desk6	50000	5000000	4374446478977598181490855431	91.821	1	2		1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	9FF67241DA6D22BE	0.137
2017-06-12T03:03:43	kkmrkkblmbrbk	c4.large	9FF67241DA6D22BE	0.137

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-06-02T00:41:39

Oliver Kruse

GTX-6

4374446478977598181490855431

5B7E8E6FBD3811__

2018-06-03T16:13:09

kracker

GRID-11

4374446478977598181490855431

5B7E8E6FBD3811__

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: 2018-06-03T16:13:09+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