M2478257 Mersenne number exponent details

is 2 ^2478257 - 1

has 746030 decimal digits

takes 0.172 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	24.0511	67.6471%	2382500	85770100	0.6965	7.5473%	24.7477	70.0888%	2.4418%
PrimeNet	2⁵⁹	0.0310	62.7119%	10000	180000	0.0019	2.5337%	0.0329	63.6566%	0.9448%
GPU72	2⁶³	0.6440	65.0794%	11000	160000	0.0019	1.3796%	0.6459	65.5611%	0.4818%
Difference	+5	+23.4071	+2.5677%	+2371500	+85610100	+0.6946	+6.1676%	+24.1017	+4.5277%	+4.5277%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2478257	46100301607563861601768129	26	85.253	9300952566171277152 2⁵ × 3 × 71 × 556067 × 2453978341	2020-05-24	556067	2453978341	3,416,379	13.500	25.115

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.234%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.785%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.263%
2011-01-21T00:06:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.378%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	120899	120899		-		-	-	0.012	-	-	0.917%
2014-10-25T09:15:00	mikr	MSI	2382500	85770100		-		-	-	0.697	-	-	7.547%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	Stephen Wood	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:15	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-14T23:40:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-08T23:44:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-08-21T01:30:00	David Campeau	Manual testing	2⁶²	2⁶³		-	-	0.396	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.792	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.508	-	-
2015-10-28T09:42:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.015	-	-
2017-07-22T20:28:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.031	-	-
2019-05-27T13:36:57	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.06	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.765 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.765 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.323	26.645%
25	50000	0.120	88.733%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	3.581
50000	5000000	46100301607563861601768129	2	0.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-11T15:06:00	Martti Järvi	Mardeni	50000	5000000						3	0.275
2010-03-22T22:25:00	James Classen	towerofart	50000	5000000						3	0.275
2012-06-06T02:22:00	smoky	mac	50000	5000000						3	0.275
2014-02-01T21:07:00	Falconiform	Falconiform	50000	5000000						3	0.275
2015-07-18T10:09:00	guru	w6	50000	5000000						3	0.275
2016-02-25T02:59:53	arnaud	CHAMOT09	50000	5000000						3	0.275
2016-06-23T07:35:31	Bruce	test	50000	5000000						3	0.275
2017-02-25T13:28:11	Bruce	eleven	50000	5000000						3	0.275
2017-10-04T23:58:58	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2017-12-20T23:27:49	Sebastian Hornbostel	V2	50000	5000000						3	0.275
2018-07-21T11:18:59	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2019-09-29T20:03:21	storm5510	3570_Ivy_Bridge	50000	5000000						3	0.275
2020-05-10T03:05:12	daveward2005	Davy	50000	5000000						3	0.275
2020-05-24T03:08:28	mnd9	office2	50000	5000000	46100301607563861601768129	85.253	2	2	2059853562236078	2	0.184

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	Stephen Wood	v4_computers	A8D3950EED4584B9	0.172
2018-05-30T00:47:10	kkmrkkblmbrbk	old	A8D3950EED4584B9	0.172

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-05-24T06:34:23

CrypticClue

cruncher

46100301607563861601768129

6118CDA70F91480B

2020-05-26T05:51:39

Luigi Morelli

9800X

46100301607563861601768129

6118CDA70F91480B

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 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120899 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-05-26T05:51:39+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