M16305847 Mersenne number exponent details

Residue

Status

L-L

B09972CF9949D5D6

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	3.6554	64.7059%	180000	2160000	0.2282	3.5596%	3.8837	65.9622%	1.2563%
PrimeNet	2⁶⁵	0.4474	63.0769%	70000	2200000	0.1475	4.3300%	0.5949	64.6757%	1.5988%
GPU72	2⁶⁹	7.3217	65.2174%	110000	3000000	0.2121	3.1812%	7.5338	66.3239%	1.1065%
Difference	-1	-3.6663	-0.5115%	+70000	-840000	+0.0162	+0.3783%	-3.6501	-0.3617%	-0.3617%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

3.6554

64.7059%

180000

2160000

0.2282

3.5596%

3.8837

65.9622%

1.2563%

PrimeNet

2⁶⁵

0.4474

63.0769%

70000

2200000

0.1475

4.3300%

0.5949

64.6757%

1.5988%

GPU72

2⁶⁹

7.3217

65.2174%

110000

3000000

0.2121

3.1812%

7.5338

66.3239%

1.1065%

Difference

-1

-3.6663

-0.5115%

+70000

-840000

+0.0162

+0.3783%

-3.6501

-0.3617%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16305847	109118357689235380231	21	66.564	3345988641045 3 × 5 × 282383 × 789941	2014-08-18	282383	789941	1.4503	0.2458	0.4557

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16305847

109118357689235380231

66.564

3345988641045
3 × 5 × 282383 × 789941

2014-08-18

282383

789941

1.4503

0.2458

0.4557

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-24T00:00:00	ANONYMOUS	v4_computers	180000	2160000		-		-	-	0.228	-	-	3.560%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.447	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2¹	2⁶⁵		-	-	0.447	-	-
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.458	-	-
2014-08-18T15:09:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷	109118357689235380231	66.564	21	0.545	18.16	1.109
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁶	2⁶⁷	109118357689235380231	66.564	21	0.545	18.16	1.109
2022-08-10T19:28:56	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.833	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-01-16T00:00:00	ANONYMOUS	v4_computers	B09972CF9949D5D6	8.916
2006-10-24T00:00:00	ANONYMOUS	v4_computers	B09972CF9949D5D6	8.916

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 = 180000, B2 = 2160000 (P-1 stage 2)

B1 = 180000 (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