M12853331 Mersenne number exponent details

Residue

Status

L-L

5C9F7DBD3565514D

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	9.2884	65.2174%	430000	8500000	0.5151	4.6573%	9.8035	66.8373%	1.6199%
PrimeNet	2⁶⁴	0.2769	62.5000%	60000	1700000	0.0885	4.3301%	0.3654	64.1238%	1.6238%
GPU72	2⁶⁸	4.6373	64.7059%	90000	2400000	0.1278	3.1636%	4.7652	65.8224%	1.1165%
Difference	+1	+4.6511	+0.5115%	+340000	+6100000	+0.3872	+1.4937%	+5.0383	+1.0149%	+1.0149%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

9.2884

65.2174%

430000

8500000

0.5151

4.6573%

9.8035

66.8373%

1.6199%

PrimeNet

2⁶⁴

0.2769

62.5000%

60000

1700000

0.0885

4.3301%

0.3654

64.1238%

1.6238%

GPU72

2⁶⁸

4.6373

64.7059%

90000

2400000

0.1278

3.1636%

4.7652

65.8224%

1.1165%

Difference

+4.6511

+0.5115%

+340000

+6100000

+0.3872

+1.4937%

+5.0383

+1.0149%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
12853331	2129206211992488057257	22	70.851	82827020170588 2² × 151 × 2111 × 64960127	2019-10-12	2111	64960127	34.408	2.0974	3.9152

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

12853331

2129206211992488057257

70.851

82827020170588
2² × 151 × 2111 × 64960127

2019-10-12

2111

64960127

34.408

2.0974

3.9152

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-06-12T00:00:00	dave_0273	v4_computers	80000	1500000		-		-	-	0.093	-	-	2.467%
2018-07-11T00:21:13	riccardo uberti	Nomad2C	430000	8500000	12	-		-	-	0.515	-	-	4.657%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.277	-	-
2013-06-03T06:44:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.291	-	-
2014-04-27T15:11:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.581	-	-
2015-04-10T11:18:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.163	-	-
2018-01-07T23:31:59	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.326	-	-
2018-01-07T23:31:59	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.651	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.242 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	1.242 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.621
50000	5000000	2129206211992488057257	1	0.621

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-04-28T00:03:10	Walter van Boer	Z87-I7-4790K	50000	5000000						1	0.621
2019-10-12T08:13:01	Keysarecool	Boat_Anchor	50000	5000000	2129206211992488057257	70.851	1	2	4803587679890376	1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-10-20T00:00:00	Lars Fricke	v4_computers	5C9F7DBD3565514D	5.250
2004-09-16T00:00:00	ANONYMOUS	v4_computers	5C9F7DBD3565514D	5.250

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-12T12:19:03

theSpirit83

i7-7700HQ

2129206211992488057257

3B4A1483C40CBB49

2020-10-05T06:54:45

Jaytholomew

2129206211992488057257

3B4A1483C40CBB49

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 = 430000, B2 = 8500000 (P-1 stage 2)

B1 = 430000 (P-1 stage 1)

B1 = 80000, B2 = 1500000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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