M2280463 Mersenne number exponent details

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is 2 ^2280463 - 1

has 686488 decimal digits

takes 0.150 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	86F91F057E3D2F15	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	2⁶⁸	26.1372	67.6471%	519022	5190220	0.0737	3.8071%	26.2109	68.8788%	1.2317%
PrimeNet	2⁵⁸	0.0168	62.0690%	10000	190000	0.0019	2.9234%	0.0187	63.1778%	1.1089%
GPU72	2⁶²	0.2694	64.5161%	12000	200000	0.0021	1.7346%	0.2715	65.1316%	0.6155%
Difference	+6	+25.8678	+3.1309%	+507022	+4990220	+0.0716	+2.0725%	+25.9394	+3.7471%	+3.7471%

Known prime factors (1 factor, 88.7 bits, 0.00388791% 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
2280463	489777554219708108832733207	27	88.662	107385551578716275781 3² × 7 × 17 × 751 × 3776239 × 35355499	2020-05-18	3776239	35355499	47,604,611	0.5240	0.7327

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.229%
2010-11-07T01:16:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-14T20:17:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.258%
2010-11-24T11:45:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.678%
2011-01-15T00:32:00	Oscar Östlin		85000	1742500		-		-	-	0.017	-	-	2.233%
2014-06-11T02:09:00	Jocelyn Larouche	Manual testing	113145	113145		-		-	-	0.011	-	-	0.869%
2014-10-06T21:12:00	Jocelyn Larouche	Manual testing	141290	141290		-		-	-	0.013	-	-	0.986%
2016-01-23T12:46:39	Jocelyn Larouche	Manual testing	519022	5190220	6	-		-	-	0.074	-	-	3.807%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15T05:38:00	Sturle Sunde	gowin.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-09T17:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.430	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.861	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.638	-	-
2015-11-01T21:51:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.277	-	-
2017-02-13T09:31:36	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	6.554	-	-
2019-09-09T13:15:03	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	13.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.505 GHz-days
Estimated T-Level:	3.200

Digits	B1	Curves	Complete	FacMiss
20	11000	64 / 100	0.640	52.560%
25	50000	64 / 280	0.229	79.534%

New Calculation Method

Total ECM effort:	5.505 GHz-days
Estimated T-Level:	3.200

Digits	B1	Complete	FacMiss
20	11000	2.065	12.688%
25	50000	0.187	82.978%
30	250000	0.011	98.858%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		63	5.419
50000	5000000	489777554219708108832733207	1	0.086

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	86F91F057E3D2F15	0.150
2018-04-27T14:47:28	kkmrkkblmbrbk	old	86F91F057E3D2F15	0.150

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-05-19T13:26:23

mnd9

75203

489777554219708108832733207

3EAB8DD4809D987C

no

2020-05-20T05:20:03

Luigi Morelli

9800X

489777554219708108832733207

3EAB8DD4809D987C

no

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 = 519022, B2 = 5190220 (P-1 stage 2)

B1 = 519022 (P-1 stage 1)

B1 = 85000, B2 = 1742500 (P-1 stage 2)

B1 = 141290 (P-1 stage 1)

B1 = 113145 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-05-20T05:20:03+00:00