M2866583 Mersenne number exponent details

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M2866583

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is 2 ^2866583 - 1

has 862928 decimal digits

takes 0.221 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	B79F38F3FC0702C3	double-checked
PRP	E4DA13D3125E475C	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.7930	67.6471%	5000000	200000000	1.7498	9.1783%	22.5428	70.6165%	2.9694%
PrimeNet	2⁵⁹	0.0268	62.7119%	13000	240000	0.0028	2.9959%	0.0296	63.8290%	1.1171%
GPU72	2⁶³	0.5568	65.0794%	16000	280000	0.0034	1.8691%	0.5602	65.7321%	0.6527%
Difference	+5	+20.2362	+2.5677%	+4984000	+199720000	+1.7464	+7.3091%	+21.9826	+4.8844%	+4.8844%

Known prime factors (1 factor, 75.2 bits, 0.00262347% 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
2866583	43518308781030623386153	23	75.204	7590624234677772 2² × 3 × 23 × 27502261719847	2020-08-02	23	27502261719847	3,369.6	167,809	313,421

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.244%
2009-07-03T00:50:00	Carsten Kossendey	leela	15000	157500		-		-	-	0.003	-	-	0.717%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-03T14:36:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.376%
2011-01-21T23:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.544%
2011-02-10T12:33:00	markr	tiny	115000	2415000		-		-	-	0.027	-	-	2.655%
2016-08-28T17:32:33	Jocelyn Larouche	low4M	153065	4830000	6	-		-	-	0.046	-	-	3.259%
2016-12-18T19:43:09	Jocelyn Larouche	low 4M	183678	183678		-		-	-	0.021	-	-	1.182%
2017-01-10T10:25:05	Jocelyn Larouche	low 4M	220413	220413		-		-	-	0.025	-	-	1.297%
2017-01-10T10:25:07	Jocelyn Larouche	low 4M	264496	264496		-		-	-	0.030	-	-	1.419%
2017-03-26T18:27:21	Jocelyn Larouche	low 4M	317395	3173950	6	-		-	-	0.053	-	-	3.307%
2017-12-21T09:19:31	Jocelyn Larouche	low 4M	634790	6347900	6	-		-	-	0.106	-	-	4.184%
2019-10-26T17:52:02	masser	Manual testing	2870000	28700000	12	-		-	-	0.479	-	-	6.421%
2020-03-13T23:19:03	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.178%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-12T19:32:00	Sturle Sunde	letov.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-01-26T10:08:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-10T10:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.342	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.685	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.303	-	-
2016-02-18T12:13:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.607	-	-
2017-11-12T17:07:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.214	-	-
2019-01-08T01:21:05	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.092 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	2.092 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.883
50000	5000000	43518308781030623386153	2	0.209

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-23T11:12:00	James Hintz	08_060209	50000	5000000						3	0.314
2010-12-06T18:49:00	Mistel		50000	5000000						3	0.314
2013-04-21T10:27:00	Donna Noble	PH2x6	50000	5000000						3	0.314
2015-07-06T19:13:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2016-09-11T03:22:01	Bruce	test	50000	5000000						3	0.314
2019-05-25T19:20:29	furkell	furkell1	50000	5000000						3	0.314
2020-08-02T20:08:38	GAN	LMS-02	50000	5000000	43518308781030623386153	75.204	2	2	7613918854588798	2	0.209

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	B79F38F3FC0702C3	0.221
2018-09-20T00:31:28	kkmrkkblmbrbk	old	B79F38F3FC0702C3	0.221

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-02T20:46:52

ATH

ec2-PRPCF

43518308781030623386153

E4DA13D3125E475C

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2870000, B2 = 28700000 (P-1 stage 2)

B1 = 2870000 (P-1 stage 1)

B1 = 634790, B2 = 6347900 (P-1 stage 2)

B1 = 634790 (P-1 stage 1)

B1 = 317395, B2 = 3173950 (P-1 stage 2)

B1 = 153065, B2 = 4830000 (P-1 stage 2)

B1 = 317395 (P-1 stage 1)

B1 = 264496 (P-1 stage 1)

B1 = 115000, B2 = 2415000 (P-1 stage 2)

B1 = 220413 (P-1 stage 1)

B1 = 183678 (P-1 stage 1)

B1 = 153065 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 157500 (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

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-02T20:46:52+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