M6439469 Mersenne number exponent details

Residue

Status

L-L

F086BF383AC0FD91

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	4.6143	65.6716%	165000	3630000	0.0961	3.8747%	4.7105	67.0018%	1.3301%
PrimeNet	2⁶²	0.0954	62.9032%	28000	650000	0.0168	3.4841%	0.1122	64.1957%	1.2925%
GPU72	2⁶⁶	2.2934	65.1515%	45000	1000000	0.0264	2.5752%	2.3198	66.0489%	0.8974%
Difference	+1	+2.3209	+0.5201%	+120000	+2630000	+0.0698	+1.2995%	+2.3907	+0.9528%	+0.9528%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.6143

65.6716%

165000

3630000

0.0961

3.8747%

4.7105

67.0018%

1.3301%

PrimeNet

2⁶²

0.0954

62.9032%

28000

650000

0.0168

3.4841%

0.1122

64.1957%

1.2925%

GPU72

2⁶⁶

2.2934

65.1515%

45000

1000000

0.0264

2.5752%

2.3198

66.0489%

0.8974%

Difference

+2.3209

+0.5201%

+120000

+2630000

+0.0698

+1.2995%

+2.3907

+0.9528%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6439469	7939524067742262047071	22	72.750	616473506413515 3 × 5 × 41098233760901	2016-10-30	5	41098233760901	152.85	608,542	1,136,587

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6439469

7939524067742262047071

72.750

616473506413515
3 × 5 × 41098233760901

2016-10-30

41098233760901

152.85

608,542

1,136,587

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-16T00:00:00	ANONYMOUS	v4_computers	25000	25000		-		-	-	0.007	-	-	0.463%
2011-08-31T06:51:00	markr	tiny	165000	3630000		-		-	-	0.096	-	-	3.875%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.095	-	-
2016-02-23T16:39:24	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.152	-	-
2014-08-02T07:16:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.305	-	-
2014-08-05T06:50:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.580	-	-
2015-10-24T21:43:21	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.160	-	-
2016-04-03T19:18:39	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.321	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.140 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	1.140 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.855
50000	5000000	7939524067742262047071	1	0.285

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-12-10T20:14:00	JimBa	Dell	50000	5000000						3	0.855
2016-10-30T14:28:19	Bruce	Desk8	50000	5000000	7939524067742262047071	72.750	1	2		1	0.285

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	F086BF383AC0FD91	1.207
2001-10-06T00:00:00	ANONYMOUS	v4_computers	F086BF383AC0FD91	1.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-16T10:51:30

Chun sung soo

jeong-woon_Jo

7939524067742262047071

7C185A3B961F79__

2018-07-15T11:17:01

kkmrkkblmbrbk

c5.large

7939524067742262047071

7C185A3B961F79__

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 = 165000, B2 = 3630000 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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