M6275327 Mersenne number exponent details

Residue

Status

L-L

CE26E4E3B96D3C0D

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	4.7350	65.6716%	160000	3480000	0.0876	3.8090%	4.8226	66.9792%	1.3076%
PrimeNet	2⁶²	0.0979	62.9032%	26000	600000	0.0147	3.3541%	0.1126	64.1475%	1.2443%
GPU72	2⁶⁶	2.3534	65.1515%	40000	900000	0.0223	2.4351%	2.3757	66.0001%	0.8486%
Difference	+1	+2.3816	+0.5201%	+120000	+2580000	+0.0653	+1.3739%	+2.4469	+0.9791%	+0.9791%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.7350

65.6716%

160000

3480000

0.0876

3.8090%

4.8226

66.9792%

1.3076%

PrimeNet

2⁶²

0.0979

62.9032%

26000

600000

0.0147

3.3541%

0.1126

64.1475%

1.2443%

GPU72

2⁶⁶

2.3534

65.1515%

40000

900000

0.0223

2.4351%

2.3757

66.0001%

0.8486%

Difference

+2.3816

+0.5201%

+120000

+2580000

+0.0653

+1.3739%

+2.4469

+0.9791%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6275327	24459320925753004457401	23	74.373	1948848317048100 2² × 3 × 5² × 13 × 1993 × 250729903	2016-08-01	1993	250729903	1,037.2	3.5108	6.5564

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6275327

24459320925753004457401

74.373

1948848317048100
2² × 3 × 5² × 13 × 1993 × 250729903

2016-08-01

1993

250729903

1,037.2

3.5108

6.5564

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-03-05T00:00:00	ANONYMOUS	v4_computers	25000	25000		-		-	-	0.006	-	-	0.460%
2011-05-30T23:37:00	markr	tiny	160000	3480000		-		-	-	0.088	-	-	3.809%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.049	-	-
1998-09-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.098	-	-
2016-02-23T16:39:21	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.156	-	-
2014-09-12T09:14:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.313	-	-
2014-09-14T19:48:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.595	-	-
2015-10-16T01:14:28	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.191	-	-
2016-03-25T09:24:59	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.382	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.250

Digits	B1	Curves	Complete	FacMiss
20	11000	5 / 100	0.050	95.099%
25	50000	5 / 280	0.018	98.227%

New Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.250

Digits	B1	Complete	FacMiss
20	11000	0.161	85.104%
25	50000	0.015	98.553%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.808
50000	5000000	24459320925753004457401	2	0.539

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-10-12T09:35:00	JimBa	Dell	50000	5000000						3	0.808
2016-08-01T15:21:42	Bruce	Desk8	50000	5000000	24459320925753004457401	74.373	2	2		2	0.539

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	Phantomas	v4_computers	CE26E4E3B96D3C0D	1.112
2001-04-21T00:00:00	ANONYMOUS	v4_computers	CE26E4E3B96D3C0D	1.112

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22T22:18:58

kkmrkkblmbrbk

c4.xlarge

24459320925753004457401

03FA5C3F242636__

2018-09-26T05:24:58

ANONYMOUS

24459320925753004457401

03FA5C3F242636__

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 = 160000, B2 = 3480000 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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