M16918007 Mersenne number exponent details

Residue

Status

L-L

A48575C47E38D936

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	3.5232	63.2353%	220000	5445000	0.4001	4.4897%	3.9233	64.8859%	1.6506%
PrimeNet	2⁶⁵	0.4312	61.5385%	80000	2400000	0.1636	4.5271%	0.5949	63.2797%	1.7412%
GPU72	2⁶⁹	7.0568	63.7681%	120000	3200000	0.2282	3.2930%	7.2850	64.9612%	1.1931%
Difference	-1	-3.5336	-0.5328%	+100000	+2245000	+0.1719	+1.1966%	-3.3617	-0.0753%	-0.0753%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

3.5232

63.2353%

220000

5445000

0.4001

4.4897%

3.9233

64.8859%

1.6506%

PrimeNet

2⁶⁵

0.4312

61.5385%

80000

2400000

0.1636

4.5271%

0.5949

63.2797%

1.7412%

GPU72

2⁶⁹

7.0568

63.7681%

120000

3200000

0.2282

3.2930%

7.2850

64.9612%

1.1931%

Difference

-1

-3.5336

-0.5328%

+100000

+2245000

+0.1719

+1.1966%

-3.3617

-0.0753%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16918007	85020681881019291551	20	66.204	2512727470825 5² × 11 × 13 × 702860831	2014-09-21	25	702860831	1.7038	30.362	56.708

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16918007

85020681881019291551

66.204

2512727470825
5² × 11 × 13 × 702860831

2014-09-21

702860831

1.7038

30.362

56.708

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-02T00:00:00	cmarble	v4_computers	220000	5445000		-		-	-	0.400	-	-	4.490%

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	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-05-13T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2002-03-10T00:00:00	Team Prime Rib	v4_computers	2¹	2⁶⁵		-	-	0.431	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2¹	2⁶⁵		-	-	0.431	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.442	-	-
2014-09-21T13:07:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷	85020681881019291551	66.204	20	0.831	18.83	1.691
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁶	2⁶⁷	85020681881019291551	66.204	20	0.831	18.83	1.691
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.767	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-02-16T00:00:00	cmarble	v4_computers	A48575C47E38D936	9.251
2006-11-28T00:00:00	ANONYMOUS	v4_computers	A48575C47E38D936	9.251

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 = 220000, B2 = 5445000 (P-1 stage 2)

B1 = 220000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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