M13192483 Mersenne number exponent details

Residue

Status

L-L

06956C9348ED9CE1

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	2.2523	64.1791%	205000	205000	0.1214	1.8273%	2.3738	64.8337%	0.6546%
PrimeNet	2⁶⁴	0.2698	62.5000%	60000	1700000	0.0885	4.3464%	0.3583	64.1299%	1.6299%
GPU72	2⁶⁸	4.5181	64.7059%	90000	2400000	0.1278	3.1757%	4.6459	65.8267%	1.1208%
Difference	-1	-2.2658	-0.5268%	+115000	-2195000	-0.0064	-1.3484%	-2.2722	-0.9930%	-0.9930%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.2523

64.1791%

205000

0.1214

1.8273%

2.3738

64.8337%

0.6546%

PrimeNet

2⁶⁴

0.2698

62.5000%

60000

1700000

0.0885

4.3464%

0.3583

64.1299%

1.6299%

GPU72

2⁶⁸

4.5181

64.7059%

90000

2400000

0.1278

3.1757%

4.6459

65.8267%

1.1208%

Difference

-1

-2.2658

-0.5268%

+115000

-2195000

-0.0064

-1.3484%

-2.2722

-0.9930%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13192483	85088399828200008669769	23	76.171	3224881920567948 2² × 3 × 2069 × 121951 × 1065091	2016-06-06	121951	1065091	1,533.7	0.1027	0.1470

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

13192483

85088399828200008669769

76.171

3224881920567948
2² × 3 × 2069 × 121951 × 1065091

2016-06-06

121951

1065091

1,533.7

0.1027

0.1470

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-01-16T00:00:00	ANONYMOUS	v4_computers	205000	205000		-		-	-	0.121	-	-	1.827%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-05-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.270	-	-
2013-05-19T20:08:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.283	-	-
2014-05-26T11:16:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.566	-	-
2015-07-14T13:29:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.133	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.621 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:	0.621 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	85088399828200008669769	1	0.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-06-06T11:04:56	Bruce	Desk2	50000	5000000	85088399828200008669769	76.171	1	2		1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-02-16T00:00:00	ANONYMOUS	v4_computers	06956C9348ED9CE1	5.389
2005-01-10T00:00:00	ANONYMOUS	v4_computers	06956C9348ED9CE1	5.389

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 = 205000 (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