M5153257 Mersenne number exponent details

Residue

Status

L-L

0E6EFFE9D8A56604

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	5.7660	65.6716%	55000	935000	0.0207	2.2487%	5.7867	66.4436%	0.7720%
PrimeNet	2⁶¹	0.0596	62.2951%	22000	500000	0.0097	3.4153%	0.0693	63.5828%	1.2878%
GPU72	2⁶⁵	1.4157	64.6154%	36000	800000	0.0156	2.5425%	1.4313	65.5151%	0.8997%
Difference	+2	+4.3503	+1.0563%	+19000	+135000	+0.0051	-0.2938%	+4.3554	+0.9285%	+0.9285%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.7660

65.6716%

55000

935000

0.0207

2.2487%

5.7867

66.4436%

0.7720%

PrimeNet

2⁶¹

0.0596

62.2951%

22000

500000

0.0097

3.4153%

0.0693

63.5828%

1.2878%

GPU72

2⁶⁵

1.4157

64.6154%

36000

800000

0.0156

2.5425%

1.4313

65.5151%

0.8997%

Difference

+4.3503

+1.0563%

+19000

+135000

+0.0051

-0.2938%

+4.3554

+0.9285%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5153257	115295150381575580299314553	27	86.575	11186629192137669468 2² × 3 × 11 × 19 × 149 × 179 × 3313 × 50479027	2014-07-26	3313	50479027	4,691,953	0.5534	1.0324

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5153257

115295150381575580299314553

86.575

11186629192137669468
2² × 3 × 11 × 19 × 149 × 179 × 3313 × 50479027

2014-07-26

3313

50479027

4,691,953

0.5534

1.0324

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-09-26T22:04:00	harlee	P4_2600	55000	935000		-		-	-	0.021	-	-	2.249%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.060	-	-
2008-10-11T16:11:00	Sturle Sunde	klengel.ifi	2⁶¹	2⁶²		-	-	0.060	-	-
2009-06-25T01:18:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.190	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.632 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:	0.632 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		115295150381575580299314553	1	0.00000e+0
50000	5000000		3	0.632

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-08-01T18:33:00	ANONYMOUS	mosura99	50000	5000000						3	0.632
2014-07-26T11:43:00	Bruce	fx6840-21			115295150381575580299314553	86.575		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-09-06T00:00:00	ANONYMOUS	v4_computers	0E6EFFE9D8A56604	0.714
2000-08-17T00:00:00	ANONYMOUS	v4_computers	0E6EFFE9D8A56604	0.714

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:15:46

kkmrkkblmbrbk

Manual testing

115295150381575580299314553

19008D8FF5EEF4__

2018-05-21T09:34:15

Oliver Kruse

GTX-4

115295150381575580299314553

19008D8FF5EEF4__

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 = 55000, B2 = 935000 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

10²

10³

10⁴

10⁵

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