M2668247 Mersenne number exponent details

Residue

Status

L-L

9EC8FFEFB7E4C469

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	11.1361	67.1642%	2000000	60000000	0.5779	7.6983%	11.7140	69.6920%	2.5278%
PrimeNet	2⁵⁹	0.0288	62.7119%	11000	200000	0.0024	2.7078%	0.0312	63.7215%	1.0097%
GPU72	2⁶³	0.5982	65.0794%	13000	220000	0.0027	1.6209%	0.6009	65.6454%	0.5660%
Difference	+4	+10.5380	+2.0848%	+1987000	+59780000	+0.5752	+6.0774%	+11.1131	+4.0466%	+4.0466%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.1361

67.1642%

2000000

60000000

0.5779

7.6983%

11.7140

69.6920%

2.5278%

PrimeNet

2⁵⁹

0.0288

62.7119%

11000

200000

0.0024

2.7078%

0.0312

63.7215%

1.0097%

GPU72

2⁶³

0.5982

65.0794%

13000

220000

0.0027

1.6209%

0.6009

65.6454%

0.5660%

Difference

+10.5380

+2.0848%

+1987000

+59780000

+0.5752

+6.0774%

+11.1131

+4.0466%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2668247	379252200277647607567	21	68.362	71067671073489 3 × 17 × 103 × 53831 × 251323	2010-07-22	53831	251323	32.857	0.0072	0.0123

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2668247

379252200277647607567

68.362

71067671073489
3 × 17 × 103 × 53831 × 251323

2010-07-22

53831

251323

32.857

0.0072

0.0123

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.296%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	213750		-		-	-	0.003	-	-	0.913%
2019-07-04T12:48:14	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 379252200277647607567	-	-	0.578	-	-	7.698%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-04-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2022-03-11T04:28:53	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.058	-	-
2009-01-31T08:29:00	Sturle Sunde	ghirardelli.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.310 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.310 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		379252200277647607567	1	0.00000e+0
50000	5000000		3	0.310

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-10T09:52:00	Csaba Vágó	home-desktop	50000	5000000						3	0.310
2010-07-22T06:14:00	SubPrime	abd0			379252200277647607567	68.362		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	9EC8FFEFB7E4C469	0.206

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

9EC8FFEFB7E4C469

0.206

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-18T15:46:39

Oliver Kruse

GTX-3

379252200277647607567

64E75732ADC770__

2017-12-03T14:12:51

kkmrkkblmbrbk

c4.xlarge

379252200277647607567

64E75732ADC770__

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 = 15000, B2 = 213750 (P-1 stage 2)

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

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