M15051823 Mersenne number exponent details

Residue

Status

L-L

A2A01A97A2097006

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	127.0839	67.1233%	300000	6000000	0.4240	2.7921%	127.5079	68.0412%	0.9180%
PrimeNet	2⁶⁵	0.4847	63.0769%	65000	2000000	0.1183	4.1450%	0.6030	64.6074%	1.5305%
GPU72	2⁶⁹	7.9317	65.2174%	100000	2600000	0.1640	2.9948%	8.0957	66.2591%	1.0417%
Difference	+4	+119.1522	+1.9059%	+200000	+3400000	+0.2599	-0.2027%	+119.4121	+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

127.0839

67.1233%

300000

6000000

0.4240

2.7921%

127.5079

68.0412%

0.9180%

PrimeNet

2⁶⁵

0.4847

63.0769%

65000

2000000

0.1183

4.1450%

0.6030

64.6074%

1.5305%

GPU72

2⁶⁹

7.9317

65.2174%

100000

2600000

0.1640

2.9948%

8.0957

66.2591%

1.0417%

Difference

+119.1522

+1.9059%

+200000

+3400000

+0.2599

-0.2027%

+119.4121

+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
15051823	37463670995629700718961	23	74.988	1244489487938760 2³ × 3 × 5 × 7 × 208673 × 7099793	2022-04-14	208673	7099793	346.61	0.4056	0.5017

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15051823

37463670995629700718961

74.988

1244489487938760
2³ × 3 × 5 × 7 × 208673 × 7099793

2022-04-14

208673

7099793

346.61

0.4056

0.5017

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-07-14T00:00:00	curtisc	v4_computers	225000	225000		-		-	-	0.156	-	-	0.904%
2015-09-17T22:50:00	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
2022-04-14T14:26:56	ATH	5960X	1000000	31000000	2	7	37463670995629700718961	P-1	23	74.988	2.168

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	-	-
2001-05-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.485	-	-
2014-06-11T15:21:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.496	-	-
2014-06-11T15:21:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.993	-	-
2016-02-01T15:20:07	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.986	-	-
2017-10-04T12:12:47	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.972	-	-
2020-07-12T13:12:28	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	7.943	-	-
2021-09-02T18:06:34	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.89	-	-
2021-10-09T10:08:59	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.77	-	-
2022-03-06T10:21:01	Dylan Delgado	GPU72_TF	2⁷²	2⁷³		-	-	63.55	-	-

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
2016-11-21T19:06:31	Xolotl	thunder-gpu-17	50000	5000000						1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-08-24T00:00:00	curtisc	v4_computers	A2A01A97A2097006	7.208
2005-09-22T00:00:00	davy	v4_computers	A2A01A97A2097006	7.208

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 = 31000000 (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)

10⁴

10⁵

10⁶

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