M5069551 Mersenne number exponent details

Residue

Status

L-L

07B39A149025A704

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	5.8613	65.6716%	1500000	45000000	0.7778	7.6737%	6.6391	68.3059%	2.6343%
PrimeNet	2⁶¹	0.0606	62.2951%	22000	500000	0.0097	3.4061%	0.0702	63.5794%	1.2843%
GPU72	2⁶⁵	1.4391	64.6154%	34000	700000	0.0141	2.4216%	1.4532	65.4723%	0.8569%
Difference	+2	+4.4221	+1.0563%	+1466000	+44300000	+0.7637	+5.2521%	+5.1858	+2.8336%	+2.8336%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.8613

65.6716%

1500000

45000000

0.7778

7.6737%

6.6391

68.3059%

2.6343%

PrimeNet

2⁶¹

0.0606

62.2951%

22000

500000

0.0097

3.4061%

0.0702

63.5794%

1.2843%

GPU72

2⁶⁵

1.4391

64.6154%

34000

700000

0.0141

2.4216%

1.4532

65.4723%

0.8569%

Difference

+4.4221

+1.0563%

+1466000

+44300000

+0.7637

+5.2521%

+5.1858

+2.8336%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5069551	56237020895499125479400857	26	85.540	5546548490734103028 2² × 3 × 11 × 67 × 1951 × 75167 × 4276511	2017-07-09	75167	4276511	3,047,132	0.0611	0.0875

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5069551

56237020895499125479400857

85.540

5546548490734103028
2² × 3 × 11 × 67 × 1951 × 75167 × 4276511

2017-07-09

75167

4276511

3,047,132

0.0611

0.0875

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-04T00:00:00	ANONYMOUS	v4_computers	25000	162500		-		-	-	0.007	-	-	1.109%
2009-08-13T18:02:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	2.361%
2017-07-09T08:40:56	mikr	S064	1500000	45000000	12		56237020895499125479400857	26	85.540	0.778	1.405	1.556	7.674%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	Carl	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2008-12-30T05:53:00	Sturle Sunde	bach.ifi	2⁶¹	2⁶²		-	-	0.061	-	-
2009-08-08T04:06:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.315	-	-
2016-02-23T16:39:08	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.194	-	-
2014-12-14T14:43:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.387	-	-
2014-12-14T14:43:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.737	-	-
2015-08-02T05:19:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.474	-	-
2016-05-22T18:45:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.948	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.265 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.265 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.265

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-09-13T00:05:00	ANONYMOUS	mosura99	50000	5000000						3	0.632
2014-06-25T21:04:00	S36049	Wolle4	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	E26D1959E018DA__	0.703
2001-01-28T00:00:00	ANONYMOUS	v4_computers	0F140CED4538DA__	0.703
2002-01-02T00:00:00	ANONYMOUS	v4_computers	07B39A149025A704	0.703

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:31

alpertron

Manual testing

56237020895499125479400857

F03D15CA9B32E8__

2018-01-19T08:27:47

kkmrkkblmbrbk

c4.xlarge

56237020895499125479400857

F03D15CA9B32E8__

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 = 1500000, B2 = 45000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 25000, B2 = 162500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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