M15724783 Mersenne number exponent details

Residue

Status

L-L

F2392218E121187E

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	1.8896	64.1791%	195000	4582500	0.3441	4.6874%	2.2338	65.8582%	1.6791%
PrimeNet	2⁶⁵	0.4640	63.0769%	70000	2200000	0.1475	4.3077%	0.6115	64.6674%	1.5905%
GPU72	2⁶⁹	7.5923	65.2174%	110000	2800000	0.2034	3.1172%	7.7957	66.3016%	1.0842%
Difference	-2	-5.7026	-1.0383%	+85000	+1782500	+0.1407	+1.5702%	-5.5619	-0.4435%	-0.4435%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.8896

64.1791%

195000

4582500

0.3441

4.6874%

2.2338

65.8582%

1.6791%

PrimeNet

2⁶⁵

0.4640

63.0769%

70000

2200000

0.1475

4.3077%

0.6115

64.6674%

1.5905%

GPU72

2⁶⁹

7.5923

65.2174%

110000

2800000

0.2034

3.1172%

7.7957

66.3016%

1.0842%

Difference

-2

-5.7026

-1.0383%

+85000

+1782500

+0.1407

+1.5702%

-5.5619

-0.4435%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15724783	270938040182641175263	21	67.877	8615000925057 3 × 31 × 92634418549	2016-12-28	31	92634418549	3.6905	4,001.6	7,473.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15724783

270938040182641175263

67.877

8615000925057
3 × 31 × 92634418549

2016-12-28

92634418549

3.6905

4,001.6

7,473.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-10T00:00:00	ANONYMOUS	v4_computers	195000	4582500		-		-	-	0.344	-	-	4.687%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-28T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.226	-	-
2001-04-01T00:00:00	xtreme2k	v4_computers	2¹	2⁶⁵		-	-	0.464	-	-
2016-03-16T02:29:03	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.475	-	-
2014-07-10T09:28:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.950	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	270938040182641175263	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-28T19:41:35	ATH	ec2-8x	50000	5000000	270938040182641175263	67.877	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-08-31T00:00:00	ANONYMOUS	v4_computers	F2392218E121187E	8.598
2006-05-29T00:00:00	ANONYMOUS	v4_computers	F2392218E121187E	8.598

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 = 195000, B2 = 4582500 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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