M2064529 Mersenne number exponent details

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M2064529

<<<

>>>

is 2 ^2064529 - 1

has 621486 decimal digits

takes 0.136 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	71430D9646A7283E	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	14.3926	68.6567%	182697	14094000	0.0897	4.4034%	14.4823	70.0369%	1.3802%
PrimeNet	2⁵⁸	0.0186	63.7931%	9000	160000	0.0016	2.6692%	0.0202	64.7595%	0.9664%
GPU72	2⁶²	0.2976	66.1290%	9000	130000	0.0015	1.3656%	0.2991	66.5916%	0.4625%
Difference	+5	+14.0950	+2.5277%	+173697	+13964000	+0.0882	+3.0378%	+14.1832	+3.4453%	+3.4453%

Known prime factors (2 factors, 148.0 bits, 0.00716911% 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
2064529	3128647069593017550169	22	71.406	757714488290796 2² × 3 × 2751461 × 22948853	2022-06-16	2751461	22948853	233.37	0.3672	0.5339
2064529	114706724737415066060297	24	76.602	27780361704150212 2² × 229 × 401 × 9013 × 8391289	2016-09-30	9013	8391289	11,989	0.0444	0.0814

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
2064529	3128647069593017550169 114706724737415066060297	358876858212326541957681298608281625376540193	45	148.008

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2009-07-23T22:52:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.017%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.413%
2011-01-06T23:25:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.594%
2011-01-20T17:53:00	James Heinrich	i7-920	135000	2936250		-		-	-	0.027	-	-	3.055%
2014-10-28T23:25:00	Jocelyn Larouche	Manual testing	166089	166089		-		-	-	0.016	-	-	1.210%
2016-07-07T00:37:25	Jocelyn Larouche	Manual testing	182697	5872500	12	-		-	-	0.047	-	-	3.727%
2016-09-30T05:48:23	Jocelyn Larouche	low 4M	182697	14094000	12		114706724737415066060297	24	76.602	0.090	0.271	0.179	4.403%

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	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-02T22:22:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-14T11:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.149	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.475	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.951	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.810	-	-
2015-11-03T10:10:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.620	-	-
2016-09-03T01:27:01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.239	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.163 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	3.163 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.413	24.330%
25	50000	0.131	87.754%
30	250000	0.008	99.177%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.293
50000	6672117		7	0.675
50000	6850000	3128647069593017550169	2	0.195

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-09T03:03:00	Nathan Slaven	q6600	50000	5000000						3	0.255
2009-10-29T10:58:00	SubPrime	stor	50000	5000000						3	0.255
2011-04-22T08:10:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-12T03:54:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-07-02T16:22:00	Bruce	xps630	50000	5000000						3	0.255
2015-07-17T09:24:00	guru	w6	50000	5000000						3	0.255
2016-02-19T09:25:20	Sintax	cloud2	50000	5000000						3	0.255
2016-05-10T02:41:44	Bruce	Desk6	50000	5000000						3	0.255
2016-07-20T23:18:52	Bruce	test	50000	5000000						3	0.255
2022-06-16T07:20:28	debrouxl	o9020	50000	6850000	3128647069593017550169	71.406	2	2	3096475526179464	2	0.195
2022-07-05T09:52:37	debrouxl	dl380g9-1	50000	6672117						7	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2015-11-14T02:20:10	MadPoo	Manual testing	71430D9646A7283E	0.136

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-06T11:52:05

Oliver Kruse

GTX-0

114706724737415066060297

F52A2EB239F196__

2017-11-16T01:38:15

kkmrkkblmbrbk

c4.xlarge

114706724737415066060297

F52A2EB239F196__

2022-06-21T00:54:46

some-students

GIMPS_IN_SHANGHAI

3128647069593017550169

114706724737415066060297

DD0B07CB077E1622

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 = 182697, B2 = 14094000 (P-1 stage 2)

B1 = 182697, B2 = 5872500 (P-1 stage 2)

B1 = 135000, B2 = 2936250 (P-1 stage 2)

B1 = 182697 (P-1 stage 1)

B1 = 166089 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-07-05T09:52:37+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