M15072823 Mersenne number exponent details

Residue

Status

L-L

55A6BEC5F4329202

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	2⁷⁴	253.8254	67.5676%	185000	4440000	0.3031	2.1429%	254.1285	68.2625%	0.6950%
PrimeNet	2⁶⁵	0.4840	63.0769%	65000	2000000	0.1239	4.1458%	0.6080	64.6077%	1.5308%
GPU72	2⁶⁹	7.9207	65.2174%	100000	2600000	0.1718	2.9954%	8.0924	66.2593%	1.0419%
Difference	+5	+245.9048	+2.3502%	+85000	+1840000	+0.1313	-0.8526%	+246.0361	+2.0033%	+2.0033%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁴

253.8254

67.5676%

185000

4440000

0.3031

2.1429%

254.1285

68.2625%

0.6950%

PrimeNet

2⁶⁵

0.4840

63.0769%

65000

2000000

0.1239

4.1458%

0.6080

64.6077%

1.5308%

GPU72

2⁶⁹

7.9207

65.2174%

100000

2600000

0.1718

2.9954%

8.0924

66.2593%

1.0419%

Difference

+245.9048

+2.3502%

+85000

+1840000

+0.1313

-0.8526%

+246.0361

+2.0033%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15072823	4699060851367776683017639	25	81.959	155878591932240453 3² × 31 × 293 × 1301 × 1597 × 917767	2022-07-05	1597	917767	45,804	0.0375	0.0679

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15072823

4699060851367776683017639

81.959

155878591932240453
3² × 31 × 293 × 1301 × 1597 × 917767

2022-07-05

1597

917767

45,804

0.0375

0.0679

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-10T00:00:00	ANONYMOUS	v4_computers	185000	4440000		-	MISSED FACTOR!	-	-	0.303	-	-	2.143%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-07-05T08:44:27	ATH	ec2-P_1	1000000	1000000	2	7	4699060851367776683017639	P-1	25	81.959	1.056

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-31T00:00:00	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2001-04-08T00:00:00	subgenius	v4_computers	2¹	2⁶⁵		-	-	0.484	-	-
2016-03-16T02:28:07	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.496	-	-
2014-06-11T15:22:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.992	-	-
2016-04-08T20:20:06	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.983	-	-
2017-10-06T08:46:39	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.966	-	-
2021-07-06T23:47:27	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	7.932	-	-
2021-09-02T18:20:59	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.86	-	-
2021-10-10T11:55:46	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.73	-	-
2022-01-22T14:28:01	-Anonymous-	GPU72_TF	2⁷²	2⁷³		-	-	63.46	-	-
2022-03-05T06:50:06	Yves de Wandelaar	Manual testing	2⁷³	2⁷⁴		-	-	126.9	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.763 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:	0.763 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		1	0.763

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-24T12:44:44	fireredd	ont111	50000	5000000						1	0.763

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-24T00:00:00	ANONYMOUS	v4_computers	14FD4B2A13586D__	7.559
2006-03-28T00:00:00	ANONYMOUS	v4_computers	55A6BEC5F4329202	7.559
2006-10-01T00:00:00	Team Prime Rib	v4_computers	55A6BEC5F4329202	7.559

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 = 1000000 (P-1 stage 1)

B1 = 185000, B2 = 4440000 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

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