M2586767 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	11.4869	67.1642%	2000000	60000000	0.5190	7.6739%	12.0059	69.6840%	2.5198%
PrimeNet	2⁵⁹	0.0297	62.7119%	11000	200000	0.0021	2.6924%	0.0318	63.7158%	1.0039%
GPU72	2⁶³	0.6170	65.0794%	12000	190000	0.0022	1.5061%	0.6192	65.6053%	0.5259%
Difference	+4	+10.8699	+2.0848%	+1988000	+59810000	+0.5168	+6.1679%	+11.3867	+4.0787%	+4.0787%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.4869

67.1642%

2000000

60000000

0.5190

7.6739%

12.0059

69.6840%

2.5198%

PrimeNet

2⁵⁹

0.0297

62.7119%

11000

200000

0.0021

2.6924%

0.0318

63.7158%

1.0039%

GPU72

2⁶³

0.6170

65.0794%

12000

190000

0.0022

1.5061%

0.6192

65.6053%

0.5259%

Difference

+10.8699

+2.0848%

+1988000

+59810000

+0.5168

+6.1679%

+11.3867

+4.0787%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2586767	5826749431515049	16	52.372	1126260972 2² × 3² × 79 × 131 × 3023	-	131	3023	0.0003	2.902e-5	3.092e-5
2586767	9222164505125073057151	22	72.966	1782565748118225 3² × 5² × 7 × 1131787776583	2018-03-22	25	1131787776583	714.26	6,201.7	11,583

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2586767

5826749431515049

52.372

1126260972
2² × 3² × 79 × 131 × 3023

131

3023

0.0003

2.902e-5

3.092e-5

2586767

9222164505125073057151

72.966

1782565748118225
3² × 5² × 7 × 1131787776583

2018-03-22

1131787776583

714.26

6,201.7

11,583

exponent	prime factors	composite factor	digits	bits*
2586767	5826749431515049 9222164505125073057151	53735241787575782625788183484093565399	38	125.337

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2019-07-04T12:41:41	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 5826749431515049	-	-	0.519	-	-	7.674%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.462 GHz-days
Estimated T-Level:	0.250

Digits	B1	Curves	Complete	FacMiss
20	11000	5 / 100	0.050	95.099%
25	50000	5 / 280	0.018	98.227%

New Calculation Method

Total ECM effort:	0.462 GHz-days
Estimated T-Level:	0.250

Digits	B1	Complete	FacMiss
20	11000	0.192	82.505%
25	50000	0.018	98.236%
30	250000	0.001	99.888%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.277
50000	5000000	9222164505125073057151	2	0.185

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-03-22T10:48:22	ATH	ec2-ECMCF	50000	5000000	9222164505125073057151	72.966	2	2		2	0.185
2019-08-27T13:06:33	J.R. Allen	lapacer	50000	5000000						3	0.277

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T12:04:15

Oliver Kruse

GTX-0

5826749431515049

8D43DBA874F138__

2017-12-02T04:31:01

kkmrkkblmbrbk

c4.xlarge

5826749431515049

8D43DBA874F138__

2018-03-24T12:25:55

Oliver Kruse

GTX-5

5826749431515049

9222164505125073057151

8D43DBA874F138__

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, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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