M5085019 Mersenne number exponent details

Residue

Status

L-L

1283B79B4075EDAE

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	5.8434	65.6716%	2000000	2000000	0.4020	3.8271%	6.2454	66.9854%	1.3138%
PrimeNet	2⁶¹	0.0604	62.2951%	22000	500000	0.0097	3.4078%	0.0701	63.5800%	1.2849%
GPU72	2⁶⁵	1.4347	64.6154%	34000	700000	0.0141	2.4229%	1.4489	65.4727%	0.8573%
Difference	+2	+4.4087	+1.0563%	+1966000	+1300000	+0.3878	+1.4042%	+4.7965	+1.5127%	+1.5127%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.8434

65.6716%

2000000

0.4020

3.8271%

6.2454

66.9854%

1.3138%

PrimeNet

2⁶¹

0.0604

62.2951%

22000

500000

0.0097

3.4078%

0.0701

63.5800%

1.2849%

GPU72

2⁶⁵

1.4347

64.6154%

34000

700000

0.0141

2.4229%

1.4489

65.4727%

0.8573%

Difference

+4.4087

+1.0563%

+1966000

+1300000

+0.3878

+1.4042%

+4.7965

+1.5127%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5085019	214002844239673510987209287	27	87.468	21042482264045966297 7 × 23 × 31 × 89107 × 129917 × 364193	2017-07-30	129917	364193	6,826,854	0.0287	0.0531

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5085019

214002844239673510987209287

87.468

21042482264045966297
7 × 23 × 31 × 89107 × 129917 × 364193

2017-07-30

129917

364193

6,826,854

0.0287

0.0531

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-23T00:00:00	ANONYMOUS	v4_computers	20000	20000		-		-	-	0.004	-	-	0.370%
2009-08-22T03:35:00	harlee	P4_2600	55000	907500		-		-	-	0.020	-	-	2.227%
2017-07-30T12:49:25	mikr	S069	2000000	2000000			214002844239673510987209287	27	87.468	0.402	1.410	0.804	3.827%

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	-	-
2008-12-28T12:07:00	Sturle Sunde	buxtehude.ifi	2⁶¹	2⁶²		-	-	0.060	-	-
2009-07-27T03:14:00	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	-	-
2014-09-15T00:12:00	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		-	-	2.939	-	-

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
2010-07-28T10:33:00	Lupo	tower	50000	5000000						3	0.632
2014-07-05T18:43:00	fireredd	ont111	50000	5000000						3	0.632
2017-07-27T14:15:06	bayanne	iMac	50000	5000000						3	0.632

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-11T00:00:00	netconx	v4_computers	1283B79B4075EDAE	0.705
2000-07-17T00:00:00	ANONYMOUS	v4_computers	1283B79B4075EDAE	0.705

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:53

alpertron

Manual testing

214002844239673510987209287

58454F973BA6D7__

2018-01-19T13:38:04

kkmrkkblmbrbk

c4.xlarge

214002844239673510987209287

58454F973BA6D7__

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 = 2000000 (P-1 stage 1)

B1 = 55000, B2 = 907500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

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