M5864207 Mersenne number exponent details

Residue

Status

L-L

EF00B314974CFF91

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	2⁶⁷	5.0670	65.6716%	65000	1088750	0.0310	2.4691%	5.0980	66.5192%	0.8476%
PrimeNet	2⁶²	0.1048	62.9032%	26000	600000	0.0147	3.3173%	0.1195	64.1338%	1.2306%
GPU72	2⁶⁶	2.5184	65.1515%	40000	800000	0.0209	2.3389%	2.5393	65.9666%	0.8151%
Difference	+1	+2.5486	+0.5201%	+25000	+288750	+0.0101	+0.1302%	+2.5587	+0.5527%	+0.5527%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.0670

65.6716%

65000

1088750

0.0310

2.4691%

5.0980

66.5192%

0.8476%

PrimeNet

2⁶²

0.1048

62.9032%

26000

600000

0.0147

3.3173%

0.1195

64.1338%

1.2306%

GPU72

2⁶⁶

2.5184

65.1515%

40000

800000

0.0209

2.3389%

2.5393

65.9666%

0.8151%

Difference

+2.5486

+0.5201%

+25000

+288750

+0.0101

+0.1302%

+2.5587

+0.5527%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5864207	4504745851239793540103	22	71.932	384088236588493 113 × 3399010943261	2011-05-26	113	3399010943261	127.30	47,588	88,881

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5864207

4504745851239793540103

71.932

384088236588493
113 × 3399010943261

2011-05-26

113

3399010943261

127.30

47,588

88,881

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-09-29T00:00:00	ANONYMOUS	v4_computers	25000	243750		-		-	-	0.009	-	-	1.303%
2011-04-27T19:41:00	harlee	P4_2600	65000	1088750		-		-	-	0.031	-	-	2.469%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-01T00:00:00	Sturle Sunde	v4_computers	2¹	2⁶¹		-	-	0.052	-	-
1998-06-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.105	-	-
2009-03-21T23:21:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.167	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		4504745851239793540103	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-05-26T01:55:00	JimBa	T510			4504745851239793540103	71.932		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-04T00:00:00	ANONYMOUS	v4_computers	EF00B314974CFF91	1.039
2000-12-07T00:00:00	ANONYMOUS	v4_computers	EF00B314974CFF91	1.039

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:27:42

kkmrkkblmbrbk

Manual testing

4504745851239793540103

0BA1E1563E8060__

2018-08-31T09:34:48

arnaud

stm-11-010

4504745851239793540103

0BA1E1563E8060__

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 = 65000, B2 = 1088750 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 25000, B2 = 243750 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶²

2⁶¹

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