M4451179 Mersenne number exponent details

Residue

Status

L-L

013A03C4171C007B

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	2⁶⁷	6.6755	65.6716%	2340000	201240000	2.3830	9.7901%	9.0585	69.0324%	3.3608%
PrimeNet	2⁶¹	0.0690	62.2951%	18000	360000	0.0066	2.9434%	0.0756	63.4049%	1.1098%
GPU72	2⁶⁵	1.6390	64.6154%	26000	550000	0.0099	2.0870%	1.6489	65.3539%	0.7385%
Difference	+2	+5.0365	+1.0563%	+2314000	+200690000	+2.3731	+7.7031%	+7.4096	+3.6785%	+3.6785%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.6755

65.6716%

2340000

201240000

2.3830

9.7901%

9.0585

69.0324%

3.3608%

PrimeNet

2⁶¹

0.0690

62.2951%

18000

360000

0.0066

2.9434%

0.0756

63.4049%

1.1098%

GPU72

2⁶⁵

1.6390

64.6154%

26000

550000

0.0099

2.0870%

1.6489

65.3539%

0.7385%

Difference

+5.0365

+1.0563%

+2314000

+200690000

+2.3731

+7.7031%

+7.4096

+3.6785%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4451179	12932448635355695689558342351	29	93.385	1452699232647765422325 3 × 5² × 443 × 36209 × 828067 × 1458239	2016-11-30	828067	1458239	601,361,726	0.1560	0.3048

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4451179

12932448635355695689558342351

93.385

1452699232647765422325
3 × 5² × 443 × 36209 × 828067 × 1458239

2016-11-30

828067

1458239

601,361,726

0.1560

0.3048

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-20T12:35:00	Carsten Kossendey	durandal	25000	356250		-		-	-	0.008	-	-	1.387%
2012-05-08T15:47:00	Squeeky_Squirrel	T7500_2200	135000	2733750		-		-	-	0.050	-	-	3.355%
2016-11-30T18:24:48	mikr	MSI	1800000	1800000			12932448635355695689558342351	29	93.385	0.326	1.110	0.651	3.637%
2021-08-06T00:51:15	Dylan Delgado	desktoplinux	2340000	201240000		-	skipped known factor: 12932448635355695689558342351	-	-	2.383	-	-	9.790%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-
2010-10-14T23:17:00	markr	ut	2⁶¹	2⁶²		-	-	0.069	-	-
2012-02-03T03:49:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.359	-	-
2016-02-23T16:38:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.221	-	-
2014-09-14T11:09:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.441	-	-
2014-09-14T12:44:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.839	-	-
2015-06-24T23:35:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.679	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.659 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.659 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.659

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-02T16:05:00	oodaira	Linux01	50000	5000000						3	0.553
2013-04-19T02:57:00	Donna Noble	q8200v2	50000	5000000						3	0.553
2016-09-24T08:49:33	bayanne	iMac	50000	5000000						3	0.553

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	013A03C4171C007B	0.555
1999-11-24T00:00:00	ANONYMOUS	v4_computers	013A03C4171C007B	0.555

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-17T00:55:33

kkmrkkblmbrbk

c4.xlarge

12932448635355695689558342351

71552B29850A96__

2018-02-14T13:33:55

Oliver Kruse

GTX-3

12932448635355695689558342351

71552B29850A96__

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 = 2340000, B2 = 201240000 (P-1 stage 2)

B1 = 2340000 (P-1 stage 1)

B1 = 1800000 (P-1 stage 1)

B1 = 135000, B2 = 2733750 (P-1 stage 2)

B1 = 135000 (P-1 stage 1)

B1 = 25000, B2 = 356250 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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