M2142403 Mersenne number exponent details

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M2142403

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>>>

is 2 ^2142403 - 1

has 644928 decimal digits

takes 0.141 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	3204C279A25FFCD7	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	13.8694	67.1642%	2500000	125000000	0.8746	8.5826%	14.7441	69.9824%	2.8182%
PrimeNet	2⁵⁸	0.0179	62.0690%	9000	170000	0.0017	2.7319%	0.0196	63.1052%	1.0362%
GPU72	2⁶²	0.2868	64.5161%	10000	150000	0.0017	1.4879%	0.2884	65.0441%	0.5280%
Difference	+5	+13.5827	+2.6481%	+2490000	+124850000	+0.8730	+7.0948%	+14.4556	+4.9383%	+4.9383%

Known prime factors (1 factor, 80.7 bits, 0.00376539% 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
2142403	1923226682254020064801849	25	80.670	448848018382633908 2² × 3 × 107 × 254783 × 1372030739	2018-07-24	254783	1372030739	210,482	7.1496	13.311

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.278%
2010-11-02T22:12:00	ANONYMOUS	Manual testing	20000	20000		-		-	-	0.002	-	-	0.303%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.417%
2011-01-13T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.598%
2011-01-24T14:35:00	James Heinrich	i7-920	130000	2632500		-		-	-	0.025	-	-	2.976%
2014-10-28T23:25:00	Jocelyn Larouche	Manual testing	159959	159959		-		-	-	0.015	-	-	1.194%
2016-06-04T03:37:01	Jocelyn Larouche	Manual testing	175954	5265000	6	-		-	-	0.043	-	-	3.640%
2016-11-13T02:06:36	Jocelyn Larouche	low 4M	211144	211144		-		-	-	0.020	-	-	1.376%
2017-04-22T17:25:11	Jocelyn Larouche	low 4M	351908	3519080	6	-		-	-	0.050	-	-	3.666%
2017-04-27T04:20:46	Jocelyn Larouche	low 4M	422289	4222890	6	-		-	-	0.060	-	-	3.902%
2017-11-02T12:09:31	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.583%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:06	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T14:53:00	Sturle Sunde	foster.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2009-01-06T20:55:00	Sturle Sunde	ginjtje.ifi	2⁶¹	2⁶²		-	-	0.143	-	-
2013-09-07T11:35:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.458	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.916	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.744	-	-
2015-12-27T16:49:15	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.488	-	-
2016-10-29T15:24:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.976	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.242 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:	3.242 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		36	3.071
50000	5000000	1923226682254020064801849	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-04T20:50:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.256
2009-11-26T15:00:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.256
2011-08-04T13:13:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-23T02:05:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2014-12-31T20:45:00	arnaud	srv-630	50000	5000000						3	0.256
2015-10-28T08:32:29	lopper	i5-4670	50000	5000000						3	0.256
2015-12-09T03:00:35	guru	w1	50000	5000000						3	0.256
2016-06-15T21:45:22	Bruce	test	50000	5000000						3	0.256
2016-09-19T06:10:31	Bruce	Desk6	50000	5000000						3	0.256
2017-03-13T22:46:50	Bruce	Desk6	50000	5000000						3	0.256
2017-09-28T20:25:35	Bruce	Desk6	50000	5000000						3	0.256
2018-02-10T10:38:11	Bruce	Desk6	50000	5000000						3	0.256
2018-07-24T04:57:16	Bruce	Desk6	50000	5000000	1923226682254020064801849	80.670	2	2		2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	3204C279A25FFCD7	0.141
2018-04-07T19:21:36	kkmrkkblmbrbk	old	3204C279A25FFCD7	0.141

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-07-24T05:25:29

ATH

ec2-PRPCF

1923226682254020064801849

74E8ABE2DFD3DB__

2018-07-24T19:15:20

kkmrkkblmbrbk

c5.large

1923226682254020064801849

74E8ABE2DFD3DB__

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 = 422289, B2 = 4222890 (P-1 stage 2)

B1 = 351908, B2 = 3519080 (P-1 stage 2)

B1 = 175954, B2 = 5265000 (P-1 stage 2)

B1 = 422289 (P-1 stage 1)

B1 = 351908 (P-1 stage 1)

B1 = 130000, B2 = 2632500 (P-1 stage 2)

B1 = 211144 (P-1 stage 1)

B1 = 175954 (P-1 stage 1)

B1 = 159959 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

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

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-07-24T22:18:02+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