M15035827 Mersenne number exponent details

Residue

Status

L-L

07243A079E2EDBBE

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	63.6037	66.6667%	2000000	6630804180	252.1712	11.0123%	315.7748	70.3374%	3.6708%
PrimeNet	2⁶⁵	0.4852	63.0769%	65000	2000000	0.1183	4.1444%	0.6036	64.6072%	1.5302%
GPU72	2⁶⁹	7.9402	65.2174%	100000	2600000	0.1640	2.9944%	8.1042	66.2589%	1.0415%
Difference	+3	+55.6635	+1.4493%	+1900000	+6628204180	+252.0072	+8.0179%	+307.6707	+4.0785%	+2.6293%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

63.6037

66.6667%

2000000

6630804180

252.1712

11.0123%

315.7748

70.3374%

3.6708%

PrimeNet

2⁶⁵

0.4852

63.0769%

65000

2000000

0.1183

4.1444%

0.6036

64.6072%

1.5302%

GPU72

2⁶⁹

7.9402

65.2174%

100000

2600000

0.1640

2.9944%

8.1042

66.2589%

1.0415%

Difference

+55.6635

+1.4493%

+1900000

+6628204180

+252.0072

+8.0179%

+307.6707

+4.0785%

+2.6293%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15035827	12836076555197248609168400568787288136543	41	133.237	426849702221143160571360676362773 13 × 1327 × 6247 × 22817 × 70117 × 1104097 × 2242332973	2022-03-22	1104097	2242332973	9.918e+9	85.557	158.44

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15035827

12836076555197248609168400568787288136543

133.237

426849702221143160571360676362773
13 × 1327 × 6247 × 22817 × 70117 × 1104097 × 2242332973

2022-03-22

1104097

2242332973

9.918e+9

85.557

158.44

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-24T00:00:00	ANONYMOUS	v4_computers	165000	1938750		-		-	-	0.182	-	-	2.159%
2020-06-03T08:11:19	Tha	Z-170	500000	20000000	12	-		-	-	1.085	-	-	4.254%
2022-03-22T08:44:25	Luminescence	5950X	2000000	6630804180			12836076555197248609168400568787288136543	41	133.237	252.2	14.40	504.3	11.012%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-04-06T22:39:14	ATH	ec2-P_1	1000000	29000000	2	7			-	-	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	-	-
2001-02-04T00:00:00	kevshaw	v4_computers	2¹	2⁶⁵		-	-	0.485	-	-
2014-06-11T15:20:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.497	-	-
2014-06-11T15:20:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.994	-	-
2015-12-17T18:56:42	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.988	-	-
2017-10-01T21:35:50	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.976	-	-
2020-06-30T15:51:52	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	7.952	-	-
2021-09-02T18:02:26	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.90	-	-
2021-10-10T11:54:56	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.81	-	-

ECM factoring results:

Total ECM effort:	0.728 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	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-22T21:52:50	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-07-27T00:00:00	ANONYMOUS	v4_computers	07243A079E2EDBBE	7.200
2006-08-25T00:00:00	gurumaharashi	v4_computers	07243A079E2EDBBE	7.200

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 = 2000000, B2 = 6630804180 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 500000, B2 = 20000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 165000, B2 = 1938750 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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