M27369289 Mersenne number exponent details

Residue

Status

L-L

E5286B778D51F892

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	17.4677	64.7887%	255000	1275000	0.4169	2.5032%	17.8846	65.6701%	0.8814%
PrimeNet	2⁶⁶	0.5396	62.1212%	120000	4500000	0.4814	5.2182%	1.0210	64.0978%	1.9766%
GPU72	2⁷⁰	8.7306	64.2857%	200000	6000000	0.6926	3.9082%	9.4232	65.6815%	1.3958%
Difference	+1	+8.7371	+0.5030%	+55000	-4725000	-0.2757	-1.4050%	+8.4613	-0.0114%	-0.0114%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

17.4677

64.7887%

255000

1275000

0.4169

2.5032%

17.8846

65.6701%

0.8814%

PrimeNet

2⁶⁶

0.5396

62.1212%

120000

4500000

0.4814

5.2182%

1.0210

64.0978%

1.9766%

GPU72

2⁷⁰

8.7306

64.2857%

200000

6000000

0.6926

3.9082%

9.4232

65.6815%

1.3958%

Difference

+8.7371

+0.5030%

+55000

-4725000

-0.2757

-1.4050%

+8.4613

-0.0114%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27369289	225666382240917336679	21	67.613	4122620471451 3 × 1374206823817	2011-10-04	3	1374206823817	1.5090	100,496	187,698

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27369289

225666382240917336679

67.613

4122620471451
3 × 1374206823817

2011-10-04

1374206823817

1.5090

100,496

187,698

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2005-04-26T00:00:00	ANONYMOUS	v4_computers	255000	1275000		-		-	-	0.417	-	-	2.503%
2011-10-04T08:13:00	Carsten Kossendey	Manual testing	255000	1275000			225666382240917336679	21	67.613	0.417	50.67	0.834	2.503%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2004-04-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.011	-	-
2004-08-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.022	-	-
2004-11-03T00:00:00	Edo	v4_computers	2¹	2⁶⁷		-	-	1.086	-	-
2011-10-04T08:12:00	Carsten Kossendey	Manual testing	2⁶⁷	2⁷¹	MISSED FACTOR!	-	-	16.38	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-05-12T00:00:00	ANONYMOUS	v4_computers	E5286B778D51F892	25.34

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 = 255000, B2 = 1275000 (P-1 stage 2)

B1 = 255000 (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

TF factor-bounds graph:

2⁷¹

2⁶⁷

2⁶²

2⁶¹

2⁵⁶

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