M2455337 Mersenne number exponent details

Residue

Status

L-L

A5E1008F3EFCE37B

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	12.1018	67.1642%	2382500	85770100	0.6965	8.1874%	12.7983	69.8526%	2.6884%
PrimeNet	2⁵⁹	0.0313	62.7119%	10000	180000	0.0019	2.5293%	0.0332	63.6550%	0.9431%
GPU72	2⁶³	0.6500	65.0794%	10000	160000	0.0018	1.3339%	0.6518	65.5452%	0.4658%
Difference	+4	+11.4517	+2.0848%	+2372500	+85610100	+0.6947	+6.8535%	+12.1465	+4.3074%	+4.3074%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.1018

67.1642%

2382500

85770100

0.6965

8.1874%

12.7983

69.8526%

2.6884%

PrimeNet

2⁵⁹

0.0313

62.7119%

10000

180000

0.0019

2.5293%

0.0332

63.6550%

0.9431%

GPU72

2⁶³

0.6500

65.0794%

10000

160000

0.0018

1.3339%

0.6518

65.5452%

0.4658%

Difference

+11.4517

+2.0848%

+2372500

+85610100

+0.6947

+6.8535%

+12.1465

+4.3074%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2455337	317545602681734006694857	24	78.071	64664362301739844 2² × 7 × 9240151 × 249935473	2015-07-10	9240151	249935473	45,029	2.2482	2.5579

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2455337

317545602681734006694857

78.071

64664362301739844
2² × 7 × 9240151 × 249935473

2015-07-10

9240151

249935473

45,029

2.2482

2.5579

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	-	-	0.289%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	232500		-		-	-	0.003	-	-	0.921%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.313%
2011-01-19T14:26:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.675%
2014-05-17T07:29:00	mikr	MSI	2382500	85770100		-		-	-	0.697	-	-	8.187%
2018-09-28T17:00:42	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.633%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-08-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:52:56	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.063	-	-
2009-01-13T22:47:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-07T13:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.125	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.400	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.800	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.522	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.375 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.375 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.100
50000	5000000	317545602681734006694857	3	0.275

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T21:14:00	Battlemaxx	Maxx_mom	50000	5000000						3	0.275
2010-03-14T05:10:00	Lupo	yorick	50000	5000000						3	0.275
2012-05-12T23:17:00	omiXorp	LLB16-T5500-21	50000	5000000						3	0.275
2014-01-11T03:54:00	Andy Incline	Office-PC	50000	5000000						3	0.275
2015-07-10T11:34:00	guru	w1	50000	5000000	317545602681734006694857	78.071	3	2		3	0.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T19:44:50

Oliver Kruse

GTX-2

D2B346D589C37A__

2017-11-28T17:47:57

kkmrkkblmbrbk

c4.xlarge

317545602681734006694857

D2B346D589C37A__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

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

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 232500 (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

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