M2185409 Mersenne number exponent details

≡

M2185409

<<<

>>>

is 2 ^2185409 - 1

has 657874 decimal digits

takes 0.144 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	FD6426B781E54FEB	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	13.5965	67.1642%	2500000	125000000	0.8746	8.5993%	14.4711	69.9878%	2.8237%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8596%	0.0194	63.1536%	1.0847%
GPU72	2⁶²	0.2811	64.5161%	11000	160000	0.0018	1.5695%	0.2829	65.0731%	0.5569%
Difference	+5	+13.3154	+2.6481%	+2489000	+124840000	+0.8728	+7.0298%	+14.1882	+4.9148%	+4.9148%

Known prime factors (1 factor, 75.1 bits, 0.00343817% 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
2185409	41573561648349268474457	23	75.138	9511620398824492 2² × 13 × 182915776900471	2018-03-15	13	182915776900471	6,496.5	950,110	1,774,541

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-06T00:22:00	ANONYMOUS	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-13T08:47:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.489%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	119369	119369		-		-	-	0.011	-	-	1.022%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148738	148738		-		-	-	0.014	-	-	1.153%
2016-01-04T02:12:24	Jocelyn Larouche	Manual testing	442874	4428740	6	-		-	-	0.063	-	-	3.974%
2018-02-08T23:43:37	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.599%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-02T05:00:00	Sturle Sunde	gnom.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-09T06:32:00	Sturle Sunde	corbusier.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.449	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.898	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.710	-	-
2016-02-29T16:32:36	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.419	-	-
2016-11-24T19:46:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.839	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.994 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	2.994 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.129	32.335%
25	50000	0.102	90.299%
30	250000	0.006	99.374%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.823
50000	5000000	41573561648349268474457	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T05:12:00	paulie	iMac3.4	50000	5000000						3	0.257
2009-12-09T12:56:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.257
2011-09-01T18:12:00	Bud	annan	50000	5000000						3	0.257
2013-05-17T12:33:00	ANONYMOUS		50000	5000000						3	0.257
2015-03-03T16:50:00	Jason U	Server7	50000	5000000						3	0.257
2016-03-04T19:53:09	dragon325	Falken-i7-920	50000	5000000						3	0.257
2016-05-07T04:33:27	Bruce	Desk6	50000	5000000						3	0.257
2016-06-28T12:21:13	Bruce	test	50000	5000000						3	0.257
2016-10-31T16:10:14	Bruce	Desk6	50000	5000000						3	0.257
2017-04-13T08:38:27	Bruce	Desk6	50000	5000000						3	0.257
2017-11-03T15:10:59	Bruce	Desk6	50000	5000000						3	0.257
2018-03-16T00:50:22	Bruce	Desk6	50000	5000000	41573561648349268474457	75.138	2	2		2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	FD6426B781E54FEB	0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-03-19T20:19:53

Oliver Kruse

GTX-6

41573561648349268474457

0D7C41623C9A1D__

2018-03-20T10:23:59

kkmrkkblmbrbk

c5.large

41573561648349268474457

0D7C41623C9A1D__

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 442874, B2 = 4428740 (P-1 stage 2)

B1 = 442874 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148738 (P-1 stage 1)

B1 = 119369 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-03-20T10:23:59+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