M2358751 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	12.5973	67.1642%	2000000	60000000	0.5055	7.6017%	13.1028	69.6603%	2.4961%
PrimeNet	2⁵⁸	0.0163	62.0690%	11000	200000	0.0021	3.0507%	0.0184	63.2261%	1.1572%
GPU72	2⁶²	0.2605	64.5161%	13000	220000	0.0024	1.8368%	0.2628	65.1679%	0.6518%
Difference	+5	+12.3368	+2.6481%	+1987000	+59780000	+0.5031	+5.7649%	+12.8399	+4.4924%	+4.4924%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.5973

67.1642%

2000000

60000000

0.5055

7.6017%

13.1028

69.6603%

2.4961%

PrimeNet

2⁵⁸

0.0163

62.0690%

11000

200000

0.0021

3.0507%

0.0184

63.2261%

1.1572%

GPU72

2⁶²

0.2605

64.5161%

13000

220000

0.0024

1.8368%

0.2628

65.1679%

0.6518%

Difference

+12.3368

+2.6481%

+1987000

+59780000

+0.5031

+5.7649%

+12.8399

+4.4924%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2358751	799597718993	12	39.540	169496 2³ × 21187	-	8	21187	5.239e-8	0.0001	0.0002
2358751	18727314850481954729	20	64.022	3969752392364 2² × 11 × 136861 × 659221	2017-06-28	136861	659221	2.4292	0.0162	0.0273

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2358751

799597718993

39.540

169496
2³ × 21187

21187

5.239e-8

0.0001

0.0002

2358751

18727314850481954729

64.022

3969752392364
2² × 11 × 136861 × 659221

2017-06-28

136861

659221

2.4292

0.0162

0.0273

exponent	prime factors	composite factor	digits	bits*
2358751	799597718993 18727314850481954729	14974318237309105848016289467897	32	103.562

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2018-04-27T12:00:19	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 799597718993 skipped known factor: 18727314850481954729	-	-	0.505	-	-	7.602%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-06-28T10:12:19	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	18727314850481954729	64.022	20	0.920	0.324	1.872

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.533 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:	0.533 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.533

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-02-10T19:43:25	alpertron		50000	5000000						3	0.266
2018-09-28T16:56:30	alpertron	Manual testing	50000	5000000						3	0.266

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:24

alpertron

Manual testing

799597718993

18727314850481954729

899A080F9C9AC4__

2017-11-01T08:30:45

Oliver Kruse

GTX-1

799597718993

18727314850481954729

899A080F9C9AC4__

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

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