M2627269 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	11.3098	67.1642%	2000000	60000000	0.5779	7.6862%	11.8877	69.6880%	2.5238%
PrimeNet	2⁵⁹	0.0292	62.7119%	11000	200000	0.0024	2.7001%	0.0316	63.7187%	1.0068%
GPU72	2⁶³	0.6075	65.0794%	13000	200000	0.0026	1.5721%	0.6101	65.6283%	0.5490%
Difference	+4	+10.7023	+2.0848%	+1987000	+59800000	+0.5753	+6.1141%	+11.2776	+4.0596%	+4.0596%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.3098

67.1642%

2000000

60000000

0.5779

7.6862%

11.8877

69.6880%

2.5238%

PrimeNet

2⁵⁹

0.0292

62.7119%

11000

200000

0.0024

2.7001%

0.0316

63.7187%

1.0068%

GPU72

2⁶³

0.6075

65.0794%

13000

200000

0.0026

1.5721%

0.6101

65.6283%

0.5490%

Difference

+10.7023

+2.0848%

+1987000

+59800000

+0.5753

+6.1141%

+11.2776

+4.0596%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2627269	4093285103	10	31.931	779 19 × 41	-	19	41	1.273e-10	2.262e-6	4.331e-6
2627269	86599762518685673	17	56.265	16480947044 2² × 193 × 21348377	2015-07-21	193	21348377	0.0057	0.1303	0.2433

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2627269

4093285103

31.931

779
19 × 41

1.273e-10

2.262e-6

4.331e-6

2627269

86599762518685673

56.265

16480947044
2² × 193 × 21348377

2015-07-21

193

21348377

0.0057

0.1303

0.2433

exponent	prime factors	composite factor	digits	bits*
2627269	4093285103 86599762518685673	354477517841073824430429319	27	88.196

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2019-07-04T12:42:51	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 4093285103 skipped known factor: 86599762518685673	-	-	0.578	-	-	7.686%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-03-20T12:34:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	86599762518685673	56.265	17	0.002	0.434	0.004

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.309 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:	0.309 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	0.309

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-03-28T20:56:59	Ismo Laitela	6600K	50000	5000000						3	0.309

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-17T16:52:56

Oliver Kruse

GTX-1

4093285103

86599762518685673

BF6FBC6200E8E9__

2017-12-03T23:04:58

alan145

Bear1

4093285103

86599762518685673

BF6FBC6200E8E9__

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

TF factor-bounds graph:

2⁶⁷

2⁵⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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