M2808427 Mersenne number exponent details

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M2808427

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is 2 ^2808427 - 1

has 845421 decimal digits

takes 0.217 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	-unknown-	-unknown-
PRP	F42C6A0149251C81	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	21.2236	67.6471%	5000000	200000000	1.7498	9.1610%	22.9734	70.6109%	2.9639%
PrimeNet	2⁵⁹	0.0273	62.7119%	12000	240000	0.0027	2.9287%	0.0301	63.8039%	1.0921%
GPU72	2⁶³	0.5683	65.0794%	15000	260000	0.0032	1.7908%	0.5715	65.7047%	0.6253%
Difference	+5	+20.6553	+2.5677%	+4985000	+199740000	+1.7466	+7.3703%	+22.4019	+4.9062%	+4.9062%

Known prime factors (1 factor, 70.0 bits, 0.00249294% 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
2808427	1190791048302828626617	22	70.012	212003204694804 2² × 3³ × 709 × 2768677907	2020-09-27	709	2768677907	113.17	16.894	31.552

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	-	-	0.243%
2010-11-12T22:13:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-12-19T01:13:00	markr	tiny	110000	2447500		-		-	-	0.027	-	-	2.632%
2016-08-01T15:21:51	Jocelyn Larouche	Manual testing	182000	4895000	6	-		-	-	0.049	-	-	3.357%
2016-12-29T21:56:32	Jocelyn Larouche	low 4M	218400	218400		-		-	-	0.024	-	-	1.287%
2017-05-13T16:00:13	Jocelyn Larouche	low 4M	364000	3640000	6	-		-	-	0.061	-	-	3.463%
2019-11-12T01:51:53	BigBrother	Winston	3000000	90000000	12	-		-	-	0.867	-	-	7.839%
2019-11-13T13:54:45	masser	Manual testing	3000000	30000000	12	-		-	-	0.501	-	-	6.479%
2020-01-11T17:53:48	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.161%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-13T16:23:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-02-24T04:45:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.350	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.699	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.330	-	-
2016-02-11T09:59:19	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.661	-	-
2017-10-24T17:48:47	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.322	-	-
2018-12-30T14:49:39	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.64	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.961 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.961 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.226	29.352%
25	50000	0.111	89.513%
30	250000	0.007	99.320%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	3.857
50000	5000000	1190791048302828626617	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-20T11:21:00	Aca Arsov	backo6400	50000	5000000						3	0.313
2010-12-25T00:56:00	Lupo	yorick	50000	5000000						3	0.313
2013-03-25T12:18:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-25T04:45:00	Jason U	Server7	50000	5000000						3	0.313
2016-02-17T04:40:59	Sintax	cloud	50000	5000000						3	0.313
2016-06-01T21:48:46	lettp	Home	50000	5000000						3	0.313
2017-02-15T08:24:31	Bruce	eleven	50000	5000000						3	0.313
2017-08-22T14:52:23	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.313
2018-02-06T23:16:18	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-12-16T04:13:28	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2020-08-24T08:14:03	M. R. Mayer	nimbus	50000	5000000						7	0.730
2020-09-27T05:28:15	GAN	KL-SCH01	50000	5000000	1190791048302828626617	70.012	1	2		1	0.104

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	195477753E59DC__	0.217

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-27T11:07:30

M Miller

cruncher

1190791048302828626617

F42C6A0149251C81

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 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 3000000, B2 = 30000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 364000, B2 = 3640000 (P-1 stage 2)

B1 = 182000, B2 = 4895000 (P-1 stage 2)

B1 = 364000 (P-1 stage 1)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 218400 (P-1 stage 1)

B1 = 182000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

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: 2020-09-27T11:07:30+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