M5638247 Mersenne number exponent details

Residue

Status

L-L

1261842F11C10C80

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	5.2701	65.6716%	65000	1121250	0.0281	2.4718%	5.2981	66.5202%	0.8485%
PrimeNet	2⁶²	0.1090	62.9032%	24000	550000	0.0121	3.1743%	0.1210	64.0808%	1.1776%
GPU72	2⁶⁶	2.6193	65.1515%	36000	700000	0.0165	2.1924%	2.6359	65.9155%	0.7640%
Difference	+1	+2.6507	+0.5201%	+29000	+421250	+0.0115	+0.2794%	+2.6623	+0.6046%	+0.6046%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.2701

65.6716%

65000

1121250

0.0281

2.4718%

5.2981

66.5202%

0.8485%

PrimeNet

2⁶²

0.1090

62.9032%

24000

550000

0.0121

3.1743%

0.1210

64.0808%

1.1776%

GPU72

2⁶⁶

2.6193

65.1515%

36000

700000

0.0165

2.1924%

2.6359

65.9155%

0.7640%

Difference

+2.6507

+0.5201%

+29000

+421250

+0.0115

+0.2794%

+2.6623

+0.6046%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5638247	2275815875836549137731671	25	80.913	201819455216891805 3 × 5 × 17 × 83 × 859 × 11100731363	2015-08-31	859	11100731363	86,718	138.49	258.65

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5638247

2275815875836549137731671

80.913

201819455216891805
3 × 5 × 17 × 83 × 859 × 11100731363

2015-08-31

859

11100731363

86,718

138.49

258.65

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-08-17T00:00:00	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.005	-	-	0.378%
2001-01-14T00:00:00	FLM	v4_computers	25000	306250		-		-	-	0.009	-	-	1.387%
2011-01-25T08:58:00	harlee	P4_2600	65000	1121250		-		-	-	0.028	-	-	2.472%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.109	-	-
2009-04-13T04:26:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.174	-	-
2014-11-16T20:16:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.348	-	-
2014-11-17T00:17:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.663	-	-
2015-08-27T03:58:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.325	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.720 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:	0.720 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
		2275815875836549137731671	1	0.00000e+0
50000	5000000		3	0.720

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-03-19T13:54:00	sannerud.com	strs-w2k8h	50000	5000000						3	0.720
2015-08-31T14:26:00	Sid & Andy	Emperor_Zurg			2275815875836549137731671	80.913		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-18T00:00:00	ANONYMOUS	v4_computers	1261842F11C10C80	0.890
2001-05-27T00:00:00	ANONYMOUS	v4_computers	1261842F11C10C80	0.890

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-10T13:18:36

trebor

Laptop

2275815875836549137731671

9F599B572DC71A__

2018-04-08T03:17:53

kkmrkkblmbrbk

c5.xlarge

2275815875836549137731671

9F599B572DC71A__

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 = 65000, B2 = 1121250 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 25000, B2 = 306250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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