M5082713 Mersenne number exponent details

Residue

Status

L-L

CDB2B6E2C896E66A

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	5.8461	65.6716%	1500000	45000000	0.7778	7.6758%	6.6239	68.3066%	2.6350%
PrimeNet	2⁶¹	0.0604	62.2951%	22000	500000	0.0097	3.4076%	0.0701	63.5799%	1.2848%
GPU72	2⁶⁵	1.4354	64.6154%	34000	700000	0.0141	2.4227%	1.4495	65.4726%	0.8573%
Difference	+2	+4.4107	+1.0563%	+1466000	+44300000	+0.7637	+5.2531%	+5.1744	+2.8340%	+2.8340%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.8461

65.6716%

1500000

45000000

0.7778

7.6758%

6.6239

68.3066%

2.6350%

PrimeNet

2⁶¹

0.0604

62.2951%

22000

500000

0.0097

3.4076%

0.0701

63.5799%

1.2848%

GPU72

2⁶⁵

1.4354

64.6154%

34000

700000

0.0141

2.4227%

1.4495

65.4726%

0.8573%

Difference

+4.4107

+1.0563%

+1466000

+44300000

+0.7637

+5.2531%

+5.1744

+2.8340%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5082713	78200726017464627699597569	26	86.015	7692813465708631168 2⁷ × 61 × 719 × 18181 × 75370039	2017-07-25	18181	75370039	6,105,178	0.8288	1.5415

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5082713

78200726017464627699597569

86.015

7692813465708631168
2⁷ × 61 × 719 × 18181 × 75370039

2017-07-25

18181

75370039

6,105,178

0.8288

1.5415

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-21T03:34:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	2.227%
2017-07-25T11:35:15	mikr	S066	1500000	45000000	12		78200726017464627699597569	26	86.015	0.778	1.409	1.556	7.676%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:08	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.060	-	-
2008-12-29T01:13:00	Sturle Sunde	bruckner.ifi	2⁶¹	2⁶²		-	-	0.060	-	-
2009-08-08T04:06:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.314	-	-
2016-02-23T16:39:08	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.193	-	-
2014-09-01T13:54:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.386	-	-
2014-09-15T12:51:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.735	-	-
2015-08-03T11:44:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.470	-	-
2016-05-24T17:43:32	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.940	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-17T02:27:00	S00030	vd01	50000	5000000						3	0.632
2014-06-30T10:15:00	exhopp	9007	50000	5000000						3	0.632
2017-07-27T12:37:14	Per Jessen	earth	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-08-24T00:00:00	ANONYMOUS	v4_computers	CDB2B6E2C896E66A	0.705
2000-04-05T00:00:00	ANONYMOUS	v4_computers	CDB2B6E2C896E66A	0.705

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:49

alpertron

Manual testing

78200726017464627699597569

E07C3EFF7D976B__

2018-01-19T12:35:07

kkmrkkblmbrbk

c4.xlarge

78200726017464627699597569

E07C3EFF7D976B__

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 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 55000 (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