M15053729 Mersenne number exponent details

Residue

Status

L-L

D81EA1FB5929FCA5

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	2⁷³	127.0678	67.1233%	300000	6000000	0.4240	2.7922%	127.4918	68.0413%	0.9180%
PrimeNet	2⁶⁵	0.4846	63.0769%	65000	2000000	0.1183	4.1451%	0.6030	64.6074%	1.5305%
GPU72	2⁶⁹	7.9307	65.2174%	100000	2600000	0.1640	2.9949%	8.0947	66.2591%	1.0417%
Difference	+4	+119.1371	+1.9059%	+200000	+3400000	+0.2599	-0.2027%	+119.3970	+1.7822%	+1.7822%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

127.0678

67.1233%

300000

6000000

0.4240

2.7922%

127.4918

68.0413%

0.9180%

PrimeNet

2⁶⁵

0.4846

63.0769%

65000

2000000

0.1183

4.1451%

0.6030

64.6074%

1.5305%

GPU72

2⁶⁹

7.9307

65.2174%

100000

2600000

0.1640

2.9949%

8.0947

66.2591%

1.0417%

Difference

+119.1371

+1.9059%

+200000

+3400000

+0.2599

-0.2027%

+119.3970

+1.7822%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15053729	1921876601335398300430087	25	80.669	63833904587208867 3 × 331 × 701 × 5851 × 15673069	2022-05-26	5851	15673069	29,670	0.5968	1.1075

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15053729

1921876601335398300430087

80.669

63833904587208867
3 × 331 × 701 × 5851 × 15673069

2022-05-26

5851

15673069

29,670

0.5968

1.1075

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	225000	225000		-		-	-	0.156	-	-	0.904%
2015-07-12T22:38:00	Tha	Manual testing	300000	6000000		-		-	-	0.424	-	-	2.792%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-05-26T17:19:41	ATH	ec2-P_1	1000000	29000000	2	7	1921876601335398300430087	P-1	25	80.669	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	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2001-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.485	-	-
2014-06-11T15:22:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.496	-	-
2014-06-11T15:22:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.993	-	-
2016-02-07T17:20:07	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.986	-	-
2017-10-04T12:12:47	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.971	-	-
2020-07-14T05:31:54	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	7.942	-	-
2021-09-05T07:10:56	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.88	-	-
2021-10-09T17:49:43	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.77	-	-
2022-03-06T06:09:01	Markus K.	GPU72_TF	2⁷²	2⁷³		-	-	63.54	-	-

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	0.038	96.227%
25	50000	0.004	99.645%

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
2016-11-26T23:40:29	Bruce	test	50000	5000000						1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-05-25T00:00:00	ANONYMOUS	v4_computers	D81EA1FB5929FCA5	7.209
2006-06-13T00:00:00	ebravick	v4_computers	D81EA1FB5929FCA5	7.209

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

B1 = 300000 (P-1 stage 1)

B1 = 225000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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