M4001009 Mersenne number exponent details

Residue

Status

L-L

8489CEC389F78D42

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	2⁷⁰	59.7226	68.5714%	4600000	4600000	0.8319	3.6108%	60.5545	69.7063%	1.1348%
PrimeNet	2⁶¹	0.0768	63.9344%	16000	320000	0.0059	2.7281%	0.0827	64.9183%	0.9839%
GPU72	2⁶⁵	1.8235	66.1538%	20000	360000	0.0070	1.7035%	1.8304	66.7304%	0.5766%
Difference	+5	+57.8991	+2.4176%	+4580000	+4240000	+0.8249	+1.9073%	+58.7241	+2.9758%	+2.9758%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

59.7226

68.5714%

4600000

0.8319

3.6108%

60.5545

69.7063%

1.1348%

PrimeNet

2⁶¹

0.0768

63.9344%

16000

320000

0.0059

2.7281%

0.0827

64.9183%

0.9839%

GPU72

2⁶⁵

1.8235

66.1538%

20000

360000

0.0070

1.7035%

1.8304

66.7304%

0.5766%

Difference

+57.8991

+2.4176%

+4580000

+4240000

+0.8249

+1.9073%

+58.7241

+2.9758%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4001009	4468054945175699687104872512336047	34	111.783	558366020318337160339413447 3 × 1697 × 3917 × 6959 × 14783 × 497473 × 547121	2017-10-08	497473	547121	4.406e+10	0.0905	0.1831

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4001009

4468054945175699687104872512336047

111.783

558366020318337160339413447
3 × 1697 × 3917 × 6959 × 14783 × 497473 × 547121

2017-10-08

497473

547121

4.406e+10

0.0905

0.1831

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	Team Prime Rib	v4_computers	20000	305000		-		-	-	0.006	-	-	0.773%
2009-05-28T03:03:00	Rob_Dee	twopc	50000	937500		-		-	-	0.018	-	-	1.426%
2012-09-09T18:02:00	Squeeky_Squirrel	P4_2600	260000	6240000		-		-	-	0.106	-	-	3.168%
2017-10-08T13:30:37	mikr	S066	4600000	4600000			4468054945175699687104872512336047	34	111.783	0.832	0.998	1.664	3.611%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-16T00:00:00	GlennMaitz	v4_computers	2¹	2⁶⁰		-	-	0.038	-	-
1998-06-01T00:00:00	GlennMaitz	v4_computers	2¹	2⁶⁰		-	-	0.038	-	-
1998-06-01T00:00:00	GlennMaitz	v4_computers	2¹	2⁶¹		-	-	0.077	-	-
2009-11-02T01:52:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.399	-	-
2016-02-23T16:29:45	Mark Rose	Manual testing	2⁶¹	2⁶³		-	-	0.322	-	-
2013-07-19T08:21:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.491	-	-
2013-10-09T03:38:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.934	-	-
2015-05-15T22:09:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.868	-	-
2016-08-27T12:52:17	kkmrkkblmbrbk	Manual testing	2⁶⁶	2⁶⁷		-	-	3.735	-	-
2017-02-01T09:28:29	Smok_bmv	Manual testing	2⁶⁷	2⁶⁸		-	-	7.471	-	-
2017-08-01T15:12:58	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	14.94	-	-
2017-08-01T15:12:58	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	29.88	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.619 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:	1.619 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	1.619

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-11-19T03:34:00	alan145	Bear4	50000	5000000						3	0.540
2012-11-07T22:20:00	Donna Noble	i3-2100t	50000	5000000						3	0.540
2016-03-05T08:52:32	prime_dive	erazer	50000	5000000						3	0.540

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-07-11T00:00:00	GlennMaitz	v4_computers	8489CEC389F78D42	0.499
1999-09-30T00:00:00	ANONYMOUS	v4_computers	8489CEC389F78D42	0.499

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T16:02:17

kkmrkkblmbrbk

c4.xlarge

4468054945175699687104872512336047

CC565AE53EB942__

2018-01-05T15:44:57

Oliver Kruse

GTX-5

4468054945175699687104872512336047

CC565AE53EB942__

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 = 4600000 (P-1 stage 1)

B1 = 260000, B2 = 6240000 (P-1 stage 2)

B1 = 260000 (P-1 stage 1)

B1 = 50000, B2 = 937500 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 305000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

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