M2550139 Mersenne number exponent details

Residue

Status

L-L

64E54974C3C97821

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	11.6519	67.1642%	2000000	60000000	0.5190	7.6628%	12.1708	69.6803%	2.5161%
PrimeNet	2⁵⁹	0.0301	62.7119%	11000	200000	0.0021	2.6853%	0.0323	63.7132%	1.0013%
GPU72	2⁶³	0.6259	65.0794%	12000	180000	0.0021	1.4780%	0.6280	65.5955%	0.5161%
Difference	+4	+11.0260	+2.0848%	+1988000	+59820000	+0.5168	+6.1847%	+11.5429	+4.0848%	+4.0848%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.6519

67.1642%

2000000

60000000

0.5190

7.6628%

12.1708

69.6803%

2.5161%

PrimeNet

2⁵⁹

0.0301

62.7119%

11000

200000

0.0021

2.6853%

0.0323

63.7132%

1.0013%

GPU72

2⁶³

0.6259

65.0794%

12000

180000

0.0021

1.4780%

0.6280

65.5955%

0.5161%

Difference

+11.0260

+2.0848%

+1988000

+59820000

+0.5168

+6.1847%

+11.5429

+4.0848%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2550139	97555096856007708896233	23	76.369	19127407732678044 2² × 3² × 89 × 277 × 661 × 32604863	2015-08-09	661	32604863	10,241	0.1787	0.3337

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2550139

97555096856007708896233

76.369

19127407732678044
2² × 3² × 89 × 277 × 661 × 32604863

2015-08-09

661

32604863

10,241

0.1787

0.3337

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	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.884%
2010-12-19T21:44:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.315%
2011-01-09T14:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-02-25T09:43:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	4.387%
2019-07-04T12:40:10	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 97555096856007708896233	-	-	0.519	-	-	7.663%

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	-	-
2022-03-11T02:04:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-01-31T14:17:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-16T13:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.385	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.770	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.465	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.383 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:	1.383 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	1.106
50000	5000000	97555096856007708896233	3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T19:16:00	maxybo	CB418E216	50000	5000000						3	0.277
2010-05-03T18:13:00	unconnected	X3220--xp	50000	5000000						3	0.277
2012-10-05T03:47:00	Brian V.	dxl5420	50000	5000000						3	0.277
2014-04-10T23:35:00	Kripke	Kripke	50000	5000000						3	0.277
2015-08-09T11:00:00	guru	w1	50000	5000000	97555096856007708896233	76.369	3	2		3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	64E54974C3C97821	0.177

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

64E54974C3C97821

0.177

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T21:17:30

Oliver Kruse

GTX-2

4599291E223FA7__

2017-12-01T12:54:43

kkmrkkblmbrbk

c4.xlarge

97555096856007708896233

4599291E223FA7__

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

B1 = 2000000 (P-1 stage 1)

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

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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