M16012693 Mersenne number exponent details

Residue

Status

L-L

031181F4FF5EA36C

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	2⁶⁸	3.7224	64.7059%	240000	240000	0.1903	1.7892%	3.9126	65.3374%	0.6315%
PrimeNet	2⁶⁵	0.4556	63.0769%	70000	2200000	0.1475	4.3188%	0.6031	64.6716%	1.5947%
GPU72	2⁶⁹	7.4558	65.2174%	110000	3000000	0.2121	3.1729%	7.6678	66.3210%	1.1036%
Difference	-1	-3.7334	-0.5115%	+130000	-2760000	-0.0218	-1.3837%	-3.7552	-0.9836%	-0.9836%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

3.7224

64.7059%

240000

0.1903

1.7892%

3.9126

65.3374%

0.6315%

PrimeNet

2⁶⁵

0.4556

63.0769%

70000

2200000

0.1475

4.3188%

0.6031

64.6716%

1.5947%

GPU72

2⁶⁹

7.4558

65.2174%

110000

3000000

0.2121

3.1729%

7.6678

66.3210%

1.1036%

Difference

-1

-3.7334

-0.5115%

+130000

-2760000

-0.0218

-1.3837%

-3.7552

-0.9836%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16012693	6081801660755678946553	22	72.365	189905647374732 2² × 3 × 61 × 150091 × 1728511	2017-01-09	150091	1728511	82.376	0.1872	0.2422

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16012693

6081801660755678946553

72.365

189905647374732
2² × 3 × 61 × 150091 × 1728511

2017-01-09

150091

1728511

82.376

0.1872

0.2422

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-11-24T00:00:00	ANONYMOUS	v4_computers	240000	240000		-		-	-	0.190	-	-	1.789%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-19T14:29:00	abc	Manual testing	2¹	2⁶⁶		-	-	0.922	-	-
2013-10-28T10:05:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.933	-	-
2015-10-17T15:45:40	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.867	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	6081801660755678946553	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-01-09T23:08:50	ATH	ec2-8x	50000	5000000	6081801660755678946553	72.365	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-05-26T00:00:00	ANONYMOUS	v4_computers	031181F4FF5EA36C	8.756
2006-04-28T00:00:00	TheJudger	v4_computers	031181F4FF5EA36C	8.756

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 = 240000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

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