M19189693 Mersenne number exponent details

Residue

Status

L-L

90348C075FA06A33

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	6.2214	63.7681%	230000	5635000	0.4848	4.1698%	6.7062	65.2789%	1.5108%
PrimeNet	2⁶⁵	0.3802	61.5385%	90000	2800000	0.2197	4.8391%	0.5999	63.3997%	1.8612%
GPU72	2⁶⁹	6.2214	63.7681%	140000	4000000	0.3238	3.6067%	6.5452	65.0749%	1.3068%
Difference	-	-	-	+90000	+1635000	+0.1610	+0.5631%	+0.1610	+0.2040%	+0.2040%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

6.2214

63.7681%

230000

5635000

0.4848

4.1698%

6.7062

65.2789%

1.5108%

PrimeNet

2⁶⁵

0.3802

61.5385%

90000

2800000

0.2197

4.8391%

0.5999

63.3997%

1.8612%

GPU72

2⁶⁹

6.2214

63.7681%

140000

4000000

0.3238

3.6067%

6.5452

65.0749%

1.3068%

Difference

+90000

+1635000

+0.1610

+0.5631%

+0.1610

+0.2040%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
19189693	2827158705724343226180151	25	81.226	73663468866446775 3 × 5² × 89413 × 10984751489	2019-09-15	89413	10984751489	30,244	553.30	1,033.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

19189693

2827158705724343226180151

81.226

73663468866446775
3 × 5² × 89413 × 10984751489

2019-09-15

89413

10984751489

30,244

553.30

1,033.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-26T00:00:00	zarf	v4_computers	230000	5635000		-		-	-	0.485	-	-	4.170%

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	-	-
2002-01-15T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.004	-	-
2002-04-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.185	-	-
2002-04-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.770	-	-
2014-07-06T00:26:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.779	-	-
2014-07-06T00:26:00	Nesowa	Manual testing	2⁶⁷	2⁶⁸		-	-	1.558	-	-
2017-11-30T10:52:49	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.115	-	-

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	2827158705724343226180151	1	0.969

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-09-15T08:50:28	Keysarecool	Boat_Anchor	50000	5000000	2827158705724343226180151	81.226	1	2	4590582357714795	1	0.969

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-06-17T00:00:00	zarf	v4_computers	90348C075FA06A33	12.23
2007-04-23T00:00:00	WWU-CS	v4_computers	90348C075FA06A33	12.23

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)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁴

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