M16776817 Mersenne number exponent details

Residue

Status

L-L

57840D3392BB9D41

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	3.5528	64.7059%	255000	255000	0.2022	1.8527%	3.7550	65.3598%	0.6539%
PrimeNet	2⁶⁵	0.4349	63.0769%	70000	2400000	0.1562	4.4258%	0.5910	64.7111%	1.6341%
GPU72	2⁶⁹	7.1162	65.2174%	120000	3200000	0.2282	3.2891%	7.3444	66.3614%	1.1440%
Difference	-1	-3.5634	-0.5115%	+135000	-2945000	-0.0260	-1.4363%	-3.5894	-1.0016%	-1.0016%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

3.5528

64.7059%

255000

0.2022

1.8527%

3.7550

65.3598%

0.6539%

PrimeNet

2⁶⁵

0.4349

63.0769%

70000

2400000

0.1562

4.4258%

0.5910

64.7111%

1.6341%

GPU72

2⁶⁹

7.1162

65.2174%

120000

3200000

0.2282

3.2891%

7.3444

66.3614%

1.1440%

Difference

-1

-3.5634

-0.5115%

+135000

-2945000

-0.0260

-1.4363%

-3.5894

-1.0016%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16776817	76233837544553677081	20	66.047	2271999436620 2² × 3 × 5 × 1549 × 24445873	2014-09-16	1549	24445873	1.6207	1.0572	1.9723

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16776817

76233837544553677081

66.047

2271999436620
2² × 3 × 5 × 1549 × 24445873

2014-09-16

1549

24445873

1.6207

1.0572

1.9723

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	255000	255000		-		-	-	0.202	-	-	1.853%

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	2⁵⁹		-	-	0.005	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.435	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2¹	2⁶⁵		-	-	0.435	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.445	-	-
2014-09-16T13:08:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷	76233837544553677081	66.047	20	0.740	18.68	1.507
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁶	2⁶⁷	76233837544553677081	66.047	20	0.740	18.68	1.507
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.782	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-12-16T00:00:00	ANONYMOUS	v4_computers	57840D3392BB9D41	9.174
2007-04-23T00:00:00	ANONYMOUS	v4_computers	57840D3392BB9D41	9.174

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 = 255000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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