M27371261 Mersenne number exponent details

Residue

Status

L-L

F27BE0872C53A4B1

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	17.4664	64.7887%	155000	3216250	0.4319	2.9499%	17.8984	65.8274%	1.0387%
PrimeNet	2⁶⁶	0.5396	62.1212%	120000	4500000	0.4814	5.2182%	1.0209	64.0978%	1.9766%
GPU72	2⁷⁰	8.7300	64.2857%	200000	6000000	0.6926	3.9082%	9.4226	65.6815%	1.3958%
Difference	+1	+8.7365	+0.5030%	-45000	-2783750	-0.2607	-0.9583%	+8.4758	+0.1459%	+0.1459%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

17.4664

64.7887%

155000

3216250

0.4319

2.9499%

17.8984

65.8274%

1.0387%

PrimeNet

2⁶⁶

0.5396

62.1212%

120000

4500000

0.4814

5.2182%

1.0209

64.0978%

1.9766%

GPU72

2⁷⁰

8.7300

64.2857%

200000

6000000

0.6926

3.9082%

9.4226

65.6815%

1.3958%

Difference

+8.7365

+0.5030%

-45000

-2783750

-0.2607

-0.9583%

+8.4758

+0.1459%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27371261	286481606418342392599	21	67.957	5233255537959 3² × 581472837551	2011-11-13	9	581472837551	2.1018	42,523	79,421

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27371261

286481606418342392599

67.957

5233255537959
3² × 581472837551

2011-11-13

581472837551

2.1018

42,523

79,421

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2007-10-17T00:00:00	ANONYMOUS	v4_computers	155000	3216250		-		-	-	0.432	-	-	2.950%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-11-13T09:11:00	Carsten Kossendey	Manual testing	?	?	286481606418342392599	67.957	21	1.016	51.64	2.071
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	-	-
2005-01-10T00:00:00	JC_Herles	v4_computers	2¹	2⁶⁷		-	-	1.086	-	-
2011-11-13T09:11:00	Carsten Kossendey	Manual testing	2⁶⁷	2⁷¹	MISSED FACTOR!	-	-	16.38	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-11-13T00:00:00	ANONYMOUS	v4_computers	F27BE0872C53A4B1	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 = 155000, B2 = 3216250 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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