M15 242 419 Mersenne number exponent details

Residue

Status

L-L

D86D6489811341F2

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁴	251.0012	67.5676%	2200000	706351800	29.4989	7.4255%	280.5001	69.9758%
Target	2⁶⁹	7.8325	65.2174%	100000	13000000	0.5838	3.0004%	8.4164	66.2610%
Difference	+5	+243.1687	+2.3502%	+2100000	+693351800	+28.9150	+4.4251%	+272.0837	+3.7148%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁴

251.0012

67.5676%

2200000

706351800

29.4989

7.4255%

280.5001

69.9758%

Target

2⁶⁹

7.8325

65.2174%

100000

13000000

0.5838

3.0004%

8.4164

66.2610%

Difference

+243.1687

+2.3502%

+2100000

+693351800

+28.9150

+4.4251%

+272.0837

+3.7148%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-24	curtisc	v4_computers	225000	225000		-		-	-	0.164	-	-	0.794%
2016-10-08	Tha	Manual testing	300000	6000000	12	-		-	-	0.444	-	-	2.511%
2022-04-14	Sid & Andy	Pterodactyl	2200000	706351800		-		-	-	29.50	-	-	7.426%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-31	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2001-01-08	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.003	-	-
2001-02-04	marnes	v4_computers	2¹	2⁶⁵		-	-	0.479	-	-
2014-05-28	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.490	-	-
2014-05-28	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.981	-	-
2017-01-19	Smok_bmv	Manual testing	2⁶⁷	2⁶⁸		-	-	1.961	-	-
2017-10-11	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.922	-	-
2021-06-21	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	7.844	-	-
2021-09-07	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.69	-	-
2021-10-09	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.38	-	-
2022-02-27	TheJudger	Manual testing	2⁷²	2⁷³		-	-	62.75	-	-
2022-02-27	TheJudger	Manual testing	2⁷³	2⁷⁴		-	-	125.5	-	-

ECM factoring results:

Total ECM effort:	0.763 GHz-days
Estimated T-Level:	0.192

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		1	0.763

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-05	Xolotl	copper-cpu-09	50000	5000000						1	0.763

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-05-11	curtisc	v4_computers	D86D6489811341F2	7.644
2005-11-13	WileECoyote	v4_computers	D86D6489811341F2	7.644

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 = 2200000, B2 = 706351800 (P-1 stage 2)

B1 = 2200000 (P-1 stage 1)

B1 = 300000, B2 = 6000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 225000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁸

2⁵⁷

this exponent TF target: 69

TF double-checked to: 67.9

ECM T-Level=0.19 ~= -16-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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