M19179679 Mersenne number exponent details

Residue

Status

L-L

A039C9559D308B36

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	6.2247	63.7681%	215000	3171250	0.3476	3.6539%	6.5723	65.0920%	1.3239%
PrimeNet	2⁶⁵	0.3804	61.5385%	90000	2800000	0.2197	4.8388%	0.6001	63.3995%	1.8611%
GPU72	2⁶⁹	6.2247	63.7681%	140000	4000000	0.3238	3.6065%	6.5485	65.0748%	1.3067%
Difference	-	-	-	+75000	-828750	+0.0238	+0.0475%	+0.0238	+0.0172%	+0.0172%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

6.2247

63.7681%

215000

3171250

0.3476

3.6539%

6.5723

65.0920%

1.3239%

PrimeNet

2⁶⁵

0.3804

61.5385%

90000

2800000

0.2197

4.8388%

0.6001

63.3995%

1.8611%

GPU72

2⁶⁹

6.2247

63.7681%

140000

4000000

0.3238

3.6065%

6.5485

65.0748%

1.3067%

Difference

+75000

-828750

+0.0238

+0.0475%

+0.0238

+0.0172%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
19179679	2035500322047291573521	22	70.786	53063983032440 2³ × 5 × 29 × 45744812959	2019-09-11	29	45744812959	13.484	2,303.8	4,302.9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

19179679

2035500322047291573521

70.786

53063983032440
2³ × 5 × 29 × 45744812959

2019-09-11

45744812959

13.484

2,303.8

4,302.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-04T00:00:00	ANONYMOUS	v4_computers	215000	3171250		-		-	-	0.348	-	-	3.654%

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	-	-
2002-08-03T00:00:00	Architects Cubed	v4_computers	2¹	2⁶⁶		-	-	0.770	-	-
2014-07-06T00:25:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.779	-	-
2014-07-06T00:25:00	Nesowa	Manual testing	2⁶⁷	2⁶⁸		-	-	1.558	-	-
2017-11-28T10:46:26	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.117	-	-

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	2035500322047291573521	1	0.969

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-09-11T21:40:17	Keysarecool	HPLaptop	50000	5000000	2035500322047291573521	70.786	1	2	5673074063460318	1	0.969

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-06-06T00:00:00	ANONYMOUS	v4_computers	A039C9559D308B36	12.23
2007-04-23T00:00:00	ANONYMOUS	v4_computers	A039C9559D308B36	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 = 215000, B2 = 3171250 (P-1 stage 2)

B1 = 215000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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