M4189307 Mersenne number exponent details

Residue

Status

L-L

161148FE46F6DE53

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	7.0928	67.1642%	-	-	-	-	7.0928	67.1642%	0.0000%
PrimeNet	2⁶¹	0.0733	63.9344%	17000	340000	0.0063	2.8333%	0.0796	64.9563%	1.0219%
GPU72	2⁶⁵	1.7415	66.1538%	22000	450000	0.0082	1.8739%	1.7497	66.7881%	0.6343%
Difference	+2	+5.3513	+1.0103%	-22000	-450000	-0.0082	-1.8739%	+5.3431	+0.3761%	+0.3761%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.0928

67.1642%

7.0928

67.1642%

0.0000%

PrimeNet

2⁶¹

0.0733

63.9344%

17000

340000

0.0063

2.8333%

0.0796

64.9563%

1.0219%

GPU72

2⁶⁵

1.7415

66.1538%

22000

450000

0.0082

1.8739%

1.7497

66.7881%

0.6343%

Difference

+5.3513

+1.0103%

-22000

-450000

-0.0082

-1.8739%

+5.3431

+0.3761%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4189307	12107386914186167519	20	63.393	1445034574237 607 × 22643 × 105137	2009-08-04	22643	105137	0.5551	0.0049	0.0083
4189307	6302061532887593970223	22	72.416	752160385105173 3² × 11 × 7597579647527	2018-12-06	11	7597579647527	295.15	74,859	139,816

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4189307

12107386914186167519

63.393

1445034574237
607 × 22643 × 105137

2009-08-04

22643

105137

0.5551

0.0049

0.0083

4189307

6302061532887593970223

72.416

752160385105173
3² × 11 × 7597579647527

2018-12-06

7597579647527

295.15

74,859

139,816

exponent	prime factors	composite factor	digits	bits*
4189307	12107386914186167519 6302061532887593970223	76301497335679275028186276137137775786737	41	135.809

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-04T12:44:00	Carsten Kossendey	leela					12107386914186167519	20	63.393	-	1.045	-	0.000%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.073	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.182 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:	0.182 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	6302061532887593970223	1	0.182

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-12-06T19:54:24	ATH	ec2-ECMCF	50000	5000000	6302061532887593970223	72.416	1	2		1	0.182

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-10-21T00:00:00	ANONYMOUS	v4_computers	161148FE46F6DE53	0.522
2000-11-15T00:00:00	ANONYMOUS	v4_computers	161148FE46F6DE53	0.522

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:31:32

kkmrkkblmbrbk

Manual testing

12107386914186167519

EAA13ECA79F1EB__

2018-01-18T10:39:44

Oliver Kruse

GTX-3

12107386914186167519

EAA13ECA79F1EB__

2018-12-07T16:11:52

GunnarLu

12107386914186167519

6302061532887593970223

715D4193481BEFF2

2018-12-08T09:09:39

kkmrkkblmbrbk

c5d.large

12107386914186167519

6302061532887593970223

715D4193481BEFF2

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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