M2546443 Mersenne number exponent details

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M2546443

<<<

>>>

is 2 ^2546443 - 1

has 766556 decimal digits

takes 0.177 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	1A4828395EA6766B	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	11.6688	67.1642%	3000000	135000000	1.0250	8.9475%	12.6938	70.1022%	2.9380%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6846%	0.0323	63.7129%	1.0010%
GPU72	2⁶³	0.6268	65.0794%	12000	180000	0.0021	1.4776%	0.6289	65.5954%	0.5160%
Difference	+4	+11.0420	+2.0848%	+2988000	+134820000	+1.0229	+7.4699%	+12.0649	+4.5068%	+4.5068%

Known prime factors (1 factor, 105.6 bits, 0.00414584% 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
2546443	60280492266783634822091251995559	32	105.571	11836214725164402820344153 3 × 7 × 58427 × 530447 × 1928809 × 9428633	2018-10-06	1928809	9428633	6.795e+10	0.2351	0.3948

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.292%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.884%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.315%
2011-01-08T14:34:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-02-23T07:50:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	4.386%
2018-08-17T10:20:07	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.470%
2018-10-06T02:50:05	mikr	MSI	3000000	135000000	12		60280492266783634822091251995559	32	105.571	1.025	0.353	2.050	8.947%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-02-01T19:22:00	Sturle Sunde	letov.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T17:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.386	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.771	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.467	-	-
2015-11-08T21:02:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.935	-	-
2017-08-08T13:42:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.869	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.766 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:	2.766 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	2.766

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-14T08:54:00	Smurgs	Praca	50000	5000000						3	0.277
2010-05-26T23:30:00	lindee	amokram	50000	5000000						3	0.277
2012-10-05T14:26:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.277
2014-04-03T01:00:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-08T06:22:00	guru	w6	50000	5000000						3	0.277
2016-03-07T09:59:07	Jason U	Server7	50000	5000000						3	0.277
2016-07-31T18:19:45	S36049	Wolle5	50000	5000000						3	0.277
2017-05-19T11:39:05	Bruce	eleven	50000	5000000						3	0.277
2017-10-02T09:42:53	Lelikoid	QH	50000	5000000						3	0.277
2018-02-25T20:59:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	1A4828395EA6766B	0.177
2018-06-11T07:39:59	kkmrkkblmbrbk	old	1A4828395EA6766B	0.177

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-10-06T03:10:59

ATH

ec2-PRPCF

60280492266783634822091251995559

81D274F5D5C282__

2018-10-07T06:41:40

arnaud

stm-11-010

60280492266783634822091251995559

81D274F5D5C282__

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 = 3000000, B2 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (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)

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

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2018-10-07T06:41:40+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