M5628113 Mersenne number exponent details

Residue

Status

L-L

25600ECB498EE56F

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	5.2796	65.6716%	65000	1023750	0.0268	2.4155%	5.3064	66.5008%	0.8292%
PrimeNet	2⁶²	0.1092	62.9032%	24000	550000	0.0121	3.1734%	0.1212	64.0804%	1.1772%
GPU72	2⁶⁶	2.6240	65.1515%	36000	700000	0.0165	2.1918%	2.6406	65.9153%	0.7638%
Difference	+1	+2.6555	+0.5201%	+29000	+323750	+0.0103	+0.2237%	+2.6658	+0.5855%	+0.5855%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.2796

65.6716%

65000

1023750

0.0268

2.4155%

5.3064

66.5008%

0.8292%

PrimeNet

2⁶²

0.1092

62.9032%

24000

550000

0.0121

3.1734%

0.1212

64.0804%

1.1772%

GPU72

2⁶⁶

2.6240

65.1515%

36000

700000

0.0165

2.1918%

2.6406

65.9153%

0.7638%

Difference

+2.6555

+0.5201%

+29000

+323750

+0.0103

+0.2237%

+2.6658

+0.5855%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5628113	7941576894351309363937	22	72.750	705527491572336 2⁴ × 3 × 23 × 639064756859	2015-09-01	23	639064756859	239.67	7,972.6	14,891

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5628113

7941576894351309363937

72.750

705527491572336
2⁴ × 3 × 23 × 639064756859

2015-09-01

639064756859

239.67

7,972.6

14,891

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-06-06T07:35:00	Carsten Kossendey	leela	30000	397500		-		-	-	0.011	-	-	1.571%
2011-01-19T03:24:00	harlee	P4_2600	65000	1023750		-		-	-	0.027	-	-	2.415%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.109	-	-
2009-02-08T05:27:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.174	-	-
2014-11-15T13:11:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.349	-	-
2014-11-17T00:17:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.664	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.961 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	0.961 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.154	85.740%
25	50000	0.014	98.587%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.720
50000	5000000	7941576894351309363937	1	0.240

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-03-25T10:22:00	oodaira	Linux01	50000	5000000						3	0.720
2015-09-01T03:35:00	lopper	peremyshl	50000	5000000	7941576894351309363937	72.750	1	2		1	0.240

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	25600ECB498EE56F	0.889
2000-10-07T00:00:00	ANONYMOUS	v4_computers	25600ECB498EE56F	0.889

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:46:06

kkmrkkblmbrbk

Manual testing

7941576894351309363937

E4C161D6655844__

2018-07-15T04:14:55

Oliver Kruse

GTX-4

7941576894351309363937

E4C161D6655844__

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 = 1023750 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 30000, B2 = 397500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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