M2245739 Mersenne number exponent details

Residue

Status

L-L

51B4CC098127B924

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	13.2312	67.1642%	500000	15000000	0.1230	5.1949%	13.3542	68.8700%	1.7058%
PrimeNet	2⁵⁸	0.0171	62.0690%	10000	180000	0.0018	2.8739%	0.0189	63.1591%	1.0901%
GPU72	2⁶²	0.2736	64.5161%	11000	190000	0.0020	1.6593%	0.2755	65.1049%	0.5888%
Difference	+5	+12.9577	+2.6481%	+489000	+14810000	+0.1210	+3.5355%	+13.0787	+3.7650%	+3.7650%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.2312

67.1642%

500000

15000000

0.1230

5.1949%

13.3542

68.8700%

1.7058%

PrimeNet

2⁵⁸

0.0171

62.0690%

10000

180000

0.0018

2.8739%

0.0189

63.1591%

1.0901%

GPU72

2⁶²

0.2736

64.5161%

11000

190000

0.0020

1.6593%

0.2755

65.1049%

0.5888%

Difference

+12.9577

+2.6481%

+489000

+14810000

+0.1210

+3.5355%

+13.0787

+3.7650%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2245739	4989331022674580143	19	62.114	1110843918789 3 × 11 × 193 × 367 × 475243	2008-12-24	367	475243	0.5639	0.0025	0.0046

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2245739

4989331022674580143

62.114

1110843918789
3 × 11 × 193 × 367 × 475243

2008-12-24

367

475243

0.5639

0.0025

0.0046

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.282%
2016-04-29T20:51:12	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 4989331022674580143	-	-	0.123	-	-	5.195%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.858 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	0.858 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.385	68.071%
25	50000	0.036	96.504%
30	250000	0.002	99.776%

ECM Summary

B1	B2	factor	curves	GHz-days
		4989331022674580143	1	0.00000e+0
50000	5000000		10	0.858

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-24T17:53:00	Xyzzy	Xyzzy-YV			4989331022674580143	62.114		1		1	-
2019-01-08T12:51:59	tottenhoff	2011pc	50000	5000000						3	0.258
2022-07-11T00:55:02	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.601

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	51B4CC098127B924	0.148

date

userid

compid

res64

spent (GHz-days)

1999-02-21T00:00:00

ANONYMOUS

v4_computers

51B4CC098127B924

0.148

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T11:30:20

Oliver Kruse

GTX-1

4989331022674580143

62CA8D418BBD12__

2017-11-29T15:37:43

kkmrkkblmbrbk

c4.xlarge

4989331022674580143

62CA8D418BBD12__

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

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

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