M2006009 Mersenne number exponent details

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M2006009

<<<

>>>

is 2 ^2006009 - 1

has 603869 decimal digits

takes 0.132 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	B8F78DE81C82CE65	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	14.8125	68.6567%	4000000	200000000	1.3994	9.4452%	16.2119	71.6172%	2.9604%
PrimeNet	2⁵⁸	0.0191	63.7931%	8000	140000	0.0014	2.4803%	0.0206	64.6911%	0.8980%
GPU72	2⁶²	0.3063	66.1290%	8000	110000	0.0013	1.2374%	0.3076	66.5482%	0.4191%
Difference	+5	+14.5062	+2.5277%	+3992000	+199890000	+1.3981	+8.2078%	+15.9043	+5.0690%	+5.0690%

Known prime factors (1 factor, 88.5 bits, 0.00441062% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2006009	430885468150871155588693031	27	88.477	107398687680581481835 5 × 7 × 151 × 1531 × 117617 × 112851853	2018-12-16	117617	112851853	52,318,493	0.5968	1.0948

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.040%
2003-01-16T00:00:00	ANONYMOUS	v4_computers	30000	547500		-		-	-	0.006	-	-	1.424%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.273%
2010-11-25T01:29:00	Jocelyn Larouche	Manual testing	200600	200600		-		-	-	0.019	-	-	1.326%
2012-12-10T21:36:00	Sergiosi	Manual testing	1250000	12500000		-		-	-	0.178	-	-	5.406%
2018-06-26T10:24:51	Jocelyn Larouche	low 4M	2006009	2006009		-		-	-	0.191	-	-	3.408%
2018-07-02T22:38:24	Jocelyn Larouche	low 4M	2006009	80240360	12	-		-	-	0.598	-	-	7.833%
2018-12-16T10:07:54	mikr	MSI	4000000	200000000	12		430885468150871155588693031	27	88.477	1.399	0.264	2.799	9.445%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-02T23:55:00	Sturle Sunde	bakeng.ifi	2⁶⁰	2⁶¹		-	-	0.077	-	-
2011-12-23T19:19:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.153	-	-
2013-06-18T06:22:00	BloodIce	Manual testing	2⁶²	2⁶³		-	-	0.489	-	-
2015-03-12T10:49:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.979	-	-
2015-03-12T10:49:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.863	-	-
2015-10-28T09:42:35	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.725	-	-
2016-03-14T03:48:35	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.450	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	32.238 GHz-days
Estimated T-Level:	25.156

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	20 / 640	0.031	96.921%

New Calculation Method

Total ECM effort:	32.238 GHz-days
Estimated T-Level:	25.156

Digits	B1	Complete	FacMiss
20	11000	10.731	0.002%
25	50000	1.060	34.638%
30	250000	0.076	92.639%
35	1000000	0.004	99.554%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	23.78
250000	25000000		20	8.461

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-28T12:47:00	paulie	iMac3.4	50000	5000000						3	0.254
2009-09-03T21:02:00	JimBa	E5400	50000	5000000						3	0.254
2011-01-26T05:05:00	Jocelyn Larouche	Manual testing	50000	5000000						1	0.085
2011-10-13T05:23:00	S36049	Wolle5	50000	5000000						3	0.254
2013-05-13T17:06:00	ANONYMOUS		50000	5000000						3	0.254
2014-12-23T10:18:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.254
2015-05-08T13:58:00	BloodIce	URM2	50000	5000000						200	16.92
2015-05-14T18:07:00	BloodIce	Mjolnir4	50000	5000000						65	5.500
2015-05-26T09:39:00	BloodIce	URM2	250000	25000000						20	8.461

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2015-10-29T03:39:36	MadPoo	Manual testing	B8F78DE81C82CE65	0.132

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-12-16T17:38:10

Oliver Kruse

GTX-7

430885468150871155588693031

4F1642AC5D6F0A__

2018-12-18T19:54:54

arnaud

stm-11-010

430885468150871155588693031

4F1642AC5D6F0A7C

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 2006009, B2 = 80240360 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 2006009 (P-1 stage 1)

B1 = 1250000, B2 = 12500000 (P-1 stage 2)

B1 = 1250000 (P-1 stage 1)

B1 = 200600 (P-1 stage 1)

B1 = 30000, B2 = 547500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 3000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-12-18T19:54:54+00:00

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