M4254763 Mersenne number exponent details

Residue

Status

L-L

093C8ADC5A225E86

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	6.9837	65.6716%	30000	400000	0.0091	1.4957%	6.9928	66.1851%	0.5135%
PrimeNet	2⁶¹	0.0722	62.2951%	18000	360000	0.0066	2.9205%	0.0788	63.3963%	1.1012%
GPU72	2⁶⁵	1.7147	64.6154%	24000	450000	0.0085	1.9238%	1.7233	65.2961%	0.6807%
Difference	+2	+5.2690	+1.0563%	+6000	-50000	+0.0005	-0.4280%	+5.2695	+0.8890%	+0.8890%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.9837

65.6716%

30000

400000

0.0091

1.4957%

6.9928

66.1851%

0.5135%

PrimeNet

2⁶¹

0.0722

62.2951%

18000

360000

0.0066

2.9205%

0.0788

63.3963%

1.1012%

GPU72

2⁶⁵

1.7147

64.6154%

24000

450000

0.0085

1.9238%

1.7233

65.2961%

0.6807%

Difference

+5.2690

+1.0563%

+6000

-50000

+0.0005

-0.4280%

+5.2695

+0.8890%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4254763	2575678132901731989127210010033	31	101.023	302681739605911303300232 2³ × 17 × 27583 × 80687417123375039	2013-02-18	27583	80687417123375039	4.360e+10	795,017,604	1.485e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4254763

2575678132901731989127210010033

101.023

302681739605911303300232
2³ × 17 × 27583 × 80687417123375039

2013-02-18

27583

80687417123375039

4.360e+10

795,017,604

1.485e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22T00:00:00	ANONYMOUS	v4_computers	30000	400000		-		-	-	0.009	-	-	1.496%
2002-11-24T00:00:00	ANONYMOUS	v4_computers	30000	400000		-		-	-	0.009	-	-	1.496%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.036	-	-
2002-01-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.072	-	-
2011-01-06T08:12:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.072	-	-
2012-01-31T04:36:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.375	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.547 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:	0.547 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
		2575678132901731989127210010033	1	0.00000e+0
50000	5000000		3	0.547

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-13T08:19:00	Net_Force	Vista64	50000	5000000						3	0.547
2013-02-18T14:57:00	Xyzzy	J			2575678132901731989127210010033	101.023		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-20T00:00:00	ANONYMOUS	v4_computers	093C8ADC5A225E86	0.531
2000-11-25T00:00:00	ANONYMOUS	v4_computers	093C8ADC5A225E86	0.531

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T16:58:11

kkmrkkblmbrbk

Manual testing

2575678132901731989127210010033

CDA38EB36C50DA__

2018-01-22T14:18:00

ATH

ec2-1xf

2575678132901731989127210010033

CDA38EB36C50DA__

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 = 30000, B2 = 400000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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