M19253497 Mersenne number exponent details

Residue

Status

L-L

814DB0D6060BA083

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	2⁶⁹	6.2008	63.7681%	230000	5635000	0.4848	4.1716%	6.6856	65.2796%	1.5115%
PrimeNet	2⁶⁵	0.3789	61.5385%	90000	2800000	0.2197	4.8413%	0.5986	63.4005%	1.8621%
GPU72	2⁶⁹	6.2008	63.7681%	140000	4000000	0.3238	3.6084%	6.5246	65.0755%	1.3074%
Difference	-	-	-	+90000	+1635000	+0.1610	+0.5632%	+0.1610	+0.2041%	+0.2041%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

6.2008

63.7681%

230000

5635000

0.4848

4.1716%

6.6856

65.2796%

1.5115%

PrimeNet

2⁶⁵

0.3789

61.5385%

90000

2800000

0.2197

4.8413%

0.5986

63.4005%

1.8621%

GPU72

2⁶⁹

6.2008

63.7681%

140000

4000000

0.3238

3.6084%

6.5246

65.0755%

1.3074%

Difference

+90000

+1635000

+0.1610

+0.5632%

+0.1610

+0.2041%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
19253497	53101988605820230856537	23	75.491	1379021914975244 2² × 383 × 733 × 1228028449	2019-11-03	733	1228028449	788.33	61.847	115.51

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

19253497

53101988605820230856537

75.491

1379021914975244
2² × 383 × 733 × 1228028449

2019-11-03

733

1228028449

788.33

61.847

115.51

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-11T00:00:00	ANONYMOUS	v4_computers	230000	5635000		-		-	-	0.485	-	-	4.172%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-27T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2002-02-10T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.004	-	-
2002-06-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.767	-	-
2014-06-15T08:27:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.776	-	-
2014-06-15T08:27:00	Nesowa	Manual testing	2⁶⁷	2⁶⁸		-	-	1.552	-	-
2017-11-22T10:58:59	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.105	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.969 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:	0.969 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	53101988605820230856537	1	0.969

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-11-03T05:37:08	Keysarecool	HPLaptop	50000	5000000	53101988605820230856537	75.491	1	2	7345360905393512	1	0.969

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-05-26T00:00:00	ANONYMOUS	v4_computers	814DB0D6060BA083	12.27
2007-04-23T00:00:00	TheJudger	v4_computers	814DB0D6060BA083	12.27

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 = 230000, B2 = 5635000 (P-1 stage 2)

B1 = 230000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁵⁹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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