M2186773 Mersenne number exponent details

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M2186773

<<<

>>>

is 2 ^2186773 - 1

has 658285 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	FAE4DA81D6456C45	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	13.5880	67.1642%	2500000	125000000	0.8746	8.5998%	14.4627	69.9880%	2.8238%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8599%	0.0194	63.1538%	1.0848%
GPU72	2⁶²	0.2809	64.5161%	11000	160000	0.0018	1.5697%	0.2828	65.0731%	0.5570%
Difference	+5	+13.3071	+2.6481%	+2489000	+124840000	+0.8728	+7.0301%	+14.1799	+4.9149%	+4.9149%

Known prime factors (1 factor, 74.9 bits, 0.00342663% 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
2186773	36057667918678835818471	23	74.933	8244492665374695 3 × 5 × 2714737 × 202462649	2018-03-17	2714737	202462649	2,755.0	1.2964	1.9642

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%
2011-01-13T01:17:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.489%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119351	119351		-		-	-	0.011	-	-	1.022%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148702	148702		-		-	-	0.014	-	-	1.153%
2016-02-13T08:02:41	Jocelyn Larouche	Manual testing	442688	4426880	6	-		-	-	0.063	-	-	3.974%
2018-02-15T11:18:43	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.600%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
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	-	-
2009-01-02T21:10:00	Sturle Sunde	gnom.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-09T00:02:00	Sturle Sunde	gooch.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-12-03T13:16:00	LaurV	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		-	-	1.709	-	-
2016-01-02T13:50:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.417	-	-
2016-11-24T19:46:06	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.834	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.908 GHz-days
Estimated T-Level:	1.700

Digits	B1	Curves	Complete	FacMiss
20	11000	34 / 100	0.340	71.055%
25	50000	34 / 280	0.121	88.546%

New Calculation Method

Total ECM effort:	2.908 GHz-days
Estimated T-Level:	1.700

Digits	B1	Complete	FacMiss
20	11000	1.097	33.395%
25	50000	0.099	90.563%
30	250000	0.006	99.391%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.823
50000	5000000	36057667918678835818471	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T18:32:00	Nathan Slaven	q6600	50000	5000000						3	0.257
2010-02-09T03:01:00	Reaver	Tinka_2010	50000	5000000						3	0.257
2011-09-03T07:06:00	S36049	Wolle5	50000	5000000						3	0.257
2013-05-17T21:25:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-05T18:32:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.257
2015-12-10T05:15:05	guru	w1	50000	5000000						3	0.257
2016-03-07T10:42:08	Bruce	Desk6	50000	5000000						3	0.257
2016-06-25T12:21:13	Jason U	Server7	50000	5000000						3	0.257
2016-11-02T08:00:01	Bruce	Desk6	50000	5000000						3	0.257
2017-04-14T16:49:32	Bruce	Desk6	50000	5000000						3	0.257
2017-11-03T21:42:36	Bruce	Desk6	50000	5000000						3	0.257
2018-03-17T04:46:04	Bruce	Desk6	50000	5000000	36057667918678835818471	74.933	1	2		1	0.086

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	FAE4DA81D6456C45	0.144
1999-02-14T00:00:00	ANONYMOUS	v4_computers	FAE4DA81D6456C45	0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-03-19T11:00:15

Oliver Kruse

GTX-3

36057667918678835818471

383BA44BD1E0D6__

2018-03-20T02:00:45

kkmrkkblmbrbk

c5.large

36057667918678835818471

383BA44BD1E0D6__

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 = 442688, B2 = 4426880 (P-1 stage 2)

B1 = 442688 (P-1 stage 1)

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

B1 = 148702 (P-1 stage 1)

B1 = 119351 (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)

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

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-03-20T02:00:45+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