M6115069 Mersenne number exponent details

Residue

Status

L-L

61529704C70F65AC

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	4.8591	65.6716%	115000	2242500	0.0593	3.2713%	4.9185	66.7946%	1.1230%
PrimeNet	2⁶²	0.1005	62.9032%	26000	600000	0.0147	3.3400%	0.1152	64.1423%	1.2390%
GPU72	2⁶⁶	2.4151	65.1515%	40000	900000	0.0223	2.4247%	2.4374	65.9965%	0.8450%
Difference	+1	+2.4440	+0.5201%	+75000	+1342500	+0.0370	+0.8465%	+2.4811	+0.7981%	+0.7981%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.8591

65.6716%

115000

2242500

0.0593

3.2713%

4.9185

66.7946%

1.1230%

PrimeNet

2⁶²

0.1005

62.9032%

26000

600000

0.0147

3.3400%

0.1152

64.1423%

1.2390%

GPU72

2⁶⁶

2.4151

65.1515%

40000

900000

0.0223

2.4247%

2.4374

65.9965%

0.8450%

Difference

+2.4440

+0.5201%

+75000

+1342500

+0.0370

+0.8465%

+2.4811

+0.7981%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6115069	4880676953819303591752097	25	82.013	399069655127301392 2⁴ × 13 × 1918604111188949	2016-05-13	16	1918604111188949	259,050	26,861,523	50,169,845

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6115069

4880676953819303591752097

82.013

399069655127301392
2⁴ × 13 × 1918604111188949

2016-05-13

1918604111188949

259,050

26,861,523

50,169,845

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-01-14T00:00:00	ANONYMOUS	v4_computers	20000	75000		-		-	-	0.006	-	-	0.811%
2011-04-14T22:43:00	markr	tiny	115000	2242500		-		-	-	0.059	-	-	3.271%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.100	-	-
2016-02-23T16:39:18	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.161	-	-
2014-09-10T22:05:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.321	-	-
2014-09-18T11:03:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.611	-	-
2015-10-06T05:43:17	Bruno Victal	Manual testing	2⁶⁵	2⁶⁶		-	-	1.222	-	-
2016-03-16T23:48:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.444	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.250

Digits	B1	Curves	Complete	FacMiss
20	11000	5 / 100	0.050	95.099%
25	50000	5 / 280	0.018	98.227%

New Calculation Method

Total ECM effort:	1.347 GHz-days
Estimated T-Level:	0.250

Digits	B1	Complete	FacMiss
20	11000	0.161	85.104%
25	50000	0.015	98.553%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.808
50000	5000000	4880676953819303591752097	2	0.539

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-10-14T08:07:00	Aldo_Grid	EmachineAtom	50000	5000000						3	0.808
2016-05-13T09:27:12	Bruce	desk	50000	5000000	4880676953819303591752097	82.013	2	2		2	0.539

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	E3F60DB7B69DE6__	1.084
1999-10-15T00:00:00	ANONYMOUS	v4_computers	61529704C70F65AC	1.084
2001-01-28T00:00:00	ANONYMOUS	v4_computers	61529704C70F65AC	1.084

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:42:57

kkmrkkblmbrbk

Manual testing

4880676953819303591752097

73A44104715A91__

2018-09-17T21:07:47

ANONYMOUS

4880676953819303591752097

73A44104715A91__

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 = 115000, B2 = 2242500 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 20000, B2 = 75000 (P-1 stage 2)

B1 = 20000 (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

10¹⁴

10¹⁵

10¹⁶

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