M2541703 Mersenne number exponent details

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M2541703

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>>>

is 2 ^2541703 - 1

has 765129 decimal digits

takes 0.176 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	E49EC685D0CE6EB9	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	11.6906	67.1642%	3000000	135000000	1.0250	8.9459%	12.7156	70.1016%	2.9375%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6836%	0.0324	63.7125%	1.0007%
GPU72	2⁶³	0.6279	65.0794%	12000	180000	0.0021	1.4771%	0.6301	65.5952%	0.5158%
Difference	+4	+11.0626	+2.0848%	+2988000	+134820000	+1.0229	+7.4688%	+12.0855	+4.5065%	+4.5065%

Known prime factors (1 factor, 104.0 bits, 0.00409060% 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
2541703	19876917094504844483607443516743	32	103.971	3910157302899836149937157 3 × 23 × 197 × 3163 × 10259 × 622571 × 14239207	2018-09-08	622571	14239207	7.575e+10	0.1372	0.1457

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%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.432%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.619%
2011-04-08T03:44:00	James Heinrich	WHS	300000	8000000		-		-	-	0.072	-	-	4.385%
2018-08-11T22:21:48	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.469%
2018-09-08T14:16:26	mikr	MSI	3000000	135000000	12		19876917094504844483607443516743	32	103.971	1.025	0.353	2.050	8.946%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
1999-06-06T00:00:00	Stephan Grupp	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-27T21:12:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T11:43:00	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		-	-	0.772	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.470	-	-
2015-11-08T21:03:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.940	-	-
2017-08-08T13:42:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.880	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.765 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:	2.765 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	2.765

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T20:26:00	borkencode	CFF2DC1CD	50000	5000000						3	0.276
2010-04-28T12:59:00	Lupo	yorick	50000	5000000						3	0.276
2012-09-28T06:13:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.276
2014-06-17T15:37:00	Lukasz Wrobel	i-1	50000	5000000						3	0.276
2015-08-06T15:51:00	guru	w1	50000	5000000						3	0.276
2016-03-06T14:40:02	liceomajoranaorvieto	info7	50000	5000000						3	0.276
2016-07-17T07:32:33	lettp	Home	50000	5000000						3	0.276
2017-05-16T14:58:39	Ensigma	vps_sing	50000	5000000						3	0.276
2017-09-27T16:44:24	Sebastian Hornbostel	V2	50000	5000000						3	0.276
2018-02-17T01:35:43	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	Stephan Grupp	v4_computers	E49EC685D0CE6EB9	0.176
1999-06-06T00:00:00	Stephan Grupp	v4_computers	E49EC685D0CE6EB9	0.176
2018-06-10T00:47:36	kkmrkkblmbrbk	old	E49EC685D0CE6EB9	0.176

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-09-10T14:46:52

_p95holder_

TFL7_PRPt11-E_b

19876917094504844483607443516743

F6A72D37468816__

2018-09-11T00:37:54

trebor

Laptop

19876917094504844483607443516743

F6A72D37468816__

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 = 30000 (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: 2018-09-11T00:37:54+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