M2310167 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	12.8622	67.1642%	5000000	505000000	3.1582	10.9746%	16.0205	70.7678%	3.6036%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9304%	0.0186	63.1805%	1.1115%
GPU72	2⁶²	0.2659	64.5161%	12000	200000	0.0022	1.7390%	0.2681	65.1332%	0.6171%
Difference	+5	+12.5963	+2.6481%	+4988000	+504800000	+3.1560	+9.2355%	+15.7523	+5.6346%	+5.6346%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.8622

67.1642%

5000000

505000000

3.1582

10.9746%

16.0205

70.7678%

3.6036%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9304%

0.0186

63.1805%

1.1115%

GPU72

2⁶²

0.2659

64.5161%

12000

200000

0.0022

1.7390%

0.2681

65.1332%

0.6171%

Difference

+12.5963

+2.6481%

+4988000

+504800000

+3.1560

+9.2355%

+15.7523

+5.6346%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2310167	820354162703	12	39.577	177553 177553	-	1	177553	4.538e-8	0.0009	0.0018

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2310167

820354162703

39.577

177553
177553

177553

4.538e-8

0.0009

0.0018

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2018-02-23T18:15:27	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 820354162703	-	-	0.126	-	-	5.213%
2021-05-03T09:44:04	ViliamF	3	5000000	505000000		-	skipped known factor: 820354162703	-	-	3.158	-	-	10.975%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.266 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:	0.266 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-02-02T14:29:52	Jan S.	SATURN	50000	5000000						3	0.266

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-11T15:44:27

Oliver Kruse

GTX-1

820354162703

08354472EFAA02__

2017-11-22T22:01:34

storm5510

HP-Z220-CMT

820354162703

08354472EFAA02__

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 = 5000000, B2 = 505000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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