M18403757 Mersenne number exponent details

Residue

Status

L-L

02AB1C1E1D8AFA97

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	2⁷³	103.9377	65.7534%	220000	5335000	0.4399	2.6563%	104.3776	66.6631%	0.9097%
PrimeNet	2⁶⁵	0.3964	61.5385%	80000	2600000	0.1917	4.6557%	0.5881	63.3291%	1.7907%
GPU72	2⁶⁹	6.4871	63.7681%	130000	3600000	0.2814	3.4644%	6.7685	65.0233%	1.2552%
Difference	+4	+97.4506	+1.9853%	+90000	+1735000	+0.1584	-0.8080%	+97.6091	+1.6398%	+1.6398%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

103.9377

65.7534%

220000

5335000

0.4399

2.6563%

104.3776

66.6631%

0.9097%

PrimeNet

2⁶⁵

0.3964

61.5385%

80000

2600000

0.1917

4.6557%

0.5881

63.3291%

1.7907%

GPU72

2⁶⁹

6.4871

63.7681%

130000

3600000

0.2814

3.4644%

6.7685

65.0233%

1.2552%

Difference

+97.4506

+1.9853%

+90000

+1735000

+0.1584

-0.8080%

+97.6091

+1.6398%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-06-01T00:00:00	ANONYMOUS	v4_computers	220000	5335000		-		-	-	0.440	-	-	2.656%
2003-06-17T00:00:00	ANONYMOUS	v4_computers	220000	5335000		-		-	-	0.440	-	-	2.656%
2003-07-13T00:00:00	ANONYMOUS	v4_computers	220000	5335000		-		-	-	0.440	-	-	2.656%
2003-08-25T00:00:00	ANONYMOUS	v4_computers	220000	5335000		-		-	-	0.440	-	-	2.656%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-25T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-11-14T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.004	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.193	-	-
2002-01-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.802	-	-
2016-03-23T13:00:21	Mark Rose	Manual testing	2⁶⁶	2⁶⁷		-	-	0.812	-	-
2018-02-04T22:42:02	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	1.624	-	-
2018-02-04T22:42:02	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.248	-	-
2020-02-15T19:30:25	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	6.497	-	-
2021-09-11T16:04:33	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	12.99	-	-
2021-10-08T19:11:57	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	25.99	-	-
2021-11-12T20:13:50	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	51.97	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.925 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:	0.925 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.925

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-12-14T21:31:46	tottenhoff	2018pc	50000	5000000						1	0.925

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-07-21T00:00:00	ANONYMOUS	v4_computers	02AB1C1E1D8AFA97	11.20
2003-08-25T00:00:00	ANONYMOUS	v4_computers	02AB1C1E1D8AFA97	11.20
2006-12-18T00:00:00	TheJudger	v4_computers	02AB1C1E1D8AFA97	11.20

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 = 220000, B2 = 5335000 (P-1 stage 2)

B1 = 220000 (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