M16771999 Mersenne number exponent details

Residue

Status

L-L

FD7EEB2A36E26E4A

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	1.7716	64.1791%	100000	1950000	0.1592	3.5827%	1.9308	65.4624%	1.2833%
PrimeNet	2⁶⁵	0.4350	63.0769%	70000	2400000	0.1562	4.4256%	0.5911	64.7110%	1.6341%
GPU72	2⁶⁹	7.1182	65.2174%	120000	3200000	0.2282	3.2890%	7.3464	66.3614%	1.1440%
Difference	-2	-5.3466	-1.0383%	-20000	-1250000	-0.0690	+0.2937%	-5.4156	-0.8989%	-0.8989%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.7716

64.1791%

100000

1950000

0.1592

3.5827%

1.9308

65.4624%

1.2833%

PrimeNet

2⁶⁵

0.4350

63.0769%

70000

2400000

0.1562

4.4256%

0.5911

64.7110%

1.6341%

GPU72

2⁶⁹

7.1182

65.2174%

120000

3200000

0.2282

3.2890%

7.3464

66.3614%

1.1440%

Difference

-2

-5.3466

-1.0383%

-20000

-1250000

-0.0690

+0.2937%

-5.4156

-0.8989%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16771999	6527561440560668037991	22	72.467	194597001841005 3² × 5 × 4324377818689	2017-06-05	9	4324377818689	59.797	186,803	348,896

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16771999

6527561440560668037991

72.467

194597001841005
3² × 5 × 4324377818689

2017-06-05

4324377818689

59.797

186,803

348,896

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-11-22T00:00:00	James Heinrich	v4_computers	100000	1950000		-		-	-	0.159	-	-	3.583%
2006-09-04T00:00:00	James Heinrich	v4_computers	100000	1950000		-		-	-	0.159	-	-	3.583%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2001-07-17T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁶⁰		-	-	0.009	-	-
2002-01-08T00:00:00	Ken Warner	v4_computers	2¹	2⁶⁵		-	-	0.435	-	-
2014-03-16T00:25:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.446	-	-
2014-09-16T13:08:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.891	-	-

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	6527561440560668037991	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-06T02:18:29	ATH	ec2-1x	50000	5000000	6527561440560668037991	72.467	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-10-26T00:00:00	ANONYMOUS	v4_computers	FD7EEB2A36E26E4A	9.171
2006-04-14T00:00:00	ANONYMOUS	v4_computers	FD7EEB2A36E26E4A	9.171

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 = 100000, B2 = 1950000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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