M27315269 Mersenne number exponent details

Residue

Status

L-L

550B80D8B5D302F4

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	2⁷¹	17.5022	64.7887%	325000	8043750	1.0007	4.0060%	18.5029	66.1993%	1.4106%
PrimeNet	2⁶⁶	0.5407	62.1212%	120000	4500000	0.4814	5.2168%	1.0220	64.0973%	1.9761%
GPU72	2⁷⁰	8.7479	64.2857%	200000	6000000	0.6926	3.9072%	9.4405	65.6811%	1.3954%
Difference	+1	+8.7544	+0.5030%	+125000	+2043750	+0.3081	+0.0989%	+9.0625	+0.5182%	+0.5182%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

17.5022

64.7887%

325000

8043750

1.0007

4.0060%

18.5029

66.1993%

1.4106%

PrimeNet

2⁶⁶

0.5407

62.1212%

120000

4500000

0.4814

5.2168%

1.0220

64.0973%

1.9761%

GPU72

2⁷⁰

8.7479

64.2857%

200000

6000000

0.6926

3.9072%

9.4405

65.6811%

1.3954%

Difference

+8.7544

+0.5030%

+125000

+2043750

+0.3081

+0.0989%

+9.0625

+0.5182%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27315269	439063135093391683793	21	68.573	8036954259784 2³ × 1004619282473	2018-04-16	8	1004619282473	2.4682	73,468	137,217

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27315269

439063135093391683793

68.573

8036954259784
2³ × 1004619282473

2018-04-16

1004619282473

2.4682

73,468

137,217

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-09-04T00:00:00	ANONYMOUS	v4_computers	325000	8043750		-		-	-	1.001	-	-	4.006%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-11-05T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁴		-	-	8.78573e-5	-	-
2001-08-18T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2004-04-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.011	-	-
2004-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.022	-	-
2004-10-18T00:00:00	foxkid	v4_computers	2¹	2⁶⁷		-	-	1.088	-	-
2011-10-05T10:09:00	Carsten Kossendey	Manual testing	2⁶⁷	2⁶⁸		-	-	1.094	-	-
2018-04-16T11:49:02	VictordeHollander	Manual testing	2⁶⁸	2⁶⁹	439063135093391683793	68.573	21	0.286	51.53	0.583
2022-02-05T17:47:05	masser	Manual testing	2⁶⁹	2⁷⁰		-	-	4.377	-	-
2022-02-14T13:38:22	masser	Manual testing	2⁷⁰	2⁷¹		-	-	8.754	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2007-01-16T00:00:00	ANONYMOUS	v4_computers	550B80D8B5D302F4	25.29
2011-11-05T14:22:00	linded	W88200JPYK0-cyert	550B80D8B5D302F4	25.29

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 = 325000, B2 = 8043750 (P-1 stage 2)

B1 = 325000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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