M15015967 Mersenne number exponent details

Residue

Status

L-L

30B4290ED616483A

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	2⁷²	63.6878	66.6667%	430000	9000000	0.6228	3.5625%	64.3106	67.8542%	1.1875%
PrimeNet	2⁶⁵	0.4859	63.0769%	65000	2000000	0.1183	4.1436%	0.6042	64.6069%	1.5299%
GPU72	2⁶⁹	7.9507	65.2174%	100000	2600000	0.1640	2.9938%	8.1147	66.2587%	1.0413%
Difference	+3	+55.7371	+1.4493%	+330000	+6400000	+0.4588	+0.5687%	+56.1959	+1.5954%	+1.5954%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

63.6878

66.6667%

430000

9000000

0.6228

3.5625%

64.3106

67.8542%

1.1875%

PrimeNet

2⁶⁵

0.4859

63.0769%

65000

2000000

0.1183

4.1436%

0.6042

64.6069%

1.5299%

GPU72

2⁶⁹

7.9507

65.2174%

100000

2600000

0.1640

2.9938%

8.1147

66.2587%

1.0413%

Difference

+55.7371

+1.4493%

+330000

+6400000

+0.4588

+0.5687%

+56.1959

+1.5954%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15015967	4080070838521920386678143	25	81.755	135857745242844513 3 × 7² × 101 × 586153 × 15611143	2022-03-03	586153	15611143	34,541	0.9754	1.1031

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15015967

4080070838521920386678143

81.755

135857745242844513
3 × 7² × 101 × 586153 × 15611143

2022-03-03

586153

15611143

34,541

0.9754

1.1031

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03T00:00:00	ANONYMOUS	v4_computers	145000	688750		-		-	-	0.121	-	-	1.570%
2018-01-03T15:04:42	riccardo uberti	Duallie-2	430000	9000000	12	-		-	-	0.623	-	-	3.562%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-03-03T20:37:33	ATH	ec2-P_1	1000000	29000000	2	7	4080070838521920386678143	P-1	25	81.755	2.094

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.486	-	-
2014-06-11T15:16:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.498	-	-
2014-06-11T15:16:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.995	-	-
2015-11-03T16:50:10	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.991	-	-
2017-09-30T18:03:33	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.981	-	-
2020-06-07T14:10:27	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	7.962	-	-
2021-09-02T17:55:37	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.92	-	-
2021-10-15T18:42:43	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.85	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.728 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:	0.728 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-20T08:01:01	EthanD	EcoAurora	50000	5000000						1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-04-28T00:00:00	ANONYMOUS	v4_computers	30B4290ED616483A	7.191
2005-09-22T00:00:00	Steven Noonan	v4_computers	30B4290ED616483A	7.191

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, B2 = 29000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 430000, B2 = 9000000 (P-1 stage 2)

B1 = 430000 (P-1 stage 1)

B1 = 145000, B2 = 688750 (P-1 stage 2)

B1 = 145000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

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