M2166457 Mersenne number exponent details

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M2166457

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is 2 ^2166457 - 1

has 652169 decimal digits

takes 0.142 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	75FD5DCB70BDA01F	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	13.7154	67.1642%	2500000	125000000	0.8746	8.5920%	14.5901	69.9854%	2.8213%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8550%	0.0196	63.1519%	1.0829%
GPU72	2⁶²	0.2836	64.5161%	10000	160000	0.0017	1.5202%	0.2853	65.0555%	0.5394%
Difference	+5	+13.4319	+2.6481%	+2490000	+124840000	+0.8729	+7.0718%	+14.3048	+4.9299%	+4.9299%

Known prime factors (1 factor, 74.4 bits, 0.00343305% 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
2166457	24504236075446412425193	23	74.375	5655370975617428 2² × 13 × 739153 × 147137513	2018-03-01	739153	147137513	2,938.7	0.8309	1.4274

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2010-11-03T21:28:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.304%
2010-12-30T22:21:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.600%
2011-01-21T17:42:00	markr	tiny	120000	2370000		-		-	-	0.023	-	-	2.869%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	149626	149626		-		-	-	0.014	-	-	1.155%
2016-03-05T00:24:32	Jocelyn Larouche	Manual testing	224438	4039884	6	-		-	-	0.041	-	-	3.576%
2017-09-05T23:15:03	Jocelyn Larouche	low 4M	448876	4488760	6	-		-	-	0.064	-	-	3.988%
2018-01-09T00:46:42	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	8.592%

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	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T05:09:00	Sturle Sunde	homilius.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-08T10:54:00	Sturle Sunde	homilius.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-09-08T17:50:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.453	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.906	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.725	-	-
2015-12-30T18:01:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.449	-	-
2016-11-11T01:20:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.899	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.076 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:	3.076 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.819
50000	5000000	24504236075446412425193	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-20T12:49:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.256
2009-12-05T02:37:00	Dmitry B. Khachaturov	mgp1-1	50000	5000000						3	0.256
2011-08-23T16:21:00	S36049	Wolle5	50000	5000000						3	0.256
2013-05-09T13:43:00	Kripke	Kripke	50000	5000000						3	0.256
2015-02-04T04:46:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-10-08T21:13:23	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2016-03-02T19:46:52	Bruce	Desk6	50000	5000000						3	0.256
2016-06-20T11:39:37	Bruce	Desk6	50000	5000000						3	0.256
2016-10-11T13:48:52	Bruce	Desk6	50000	5000000						3	0.256
2017-03-28T06:22:31	Bruce	Desk6	50000	5000000						3	0.256
2017-10-23T15:32:30	Conductor	Sasha	50000	5000000						3	0.256
2018-03-02T01:20:07	Bruce	Desk6	50000	5000000	24504236075446412425193	74.375	3	2		3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	75FD5DCB70BDA01F	0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-03-02T20:31:33

-p95holder- @bopoh13

Lucius_Yorkfield

24504236075446412425193

2F14C52592ACDC__

2018-03-07T19:42:35

Oliver Kruse

GTX-6

24504236075446412425193

2F14C52592ACDC__

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 = 448876, B2 = 4488760 (P-1 stage 2)

B1 = 448876 (P-1 stage 1)

B1 = 224438, B2 = 4039884 (P-1 stage 2)

B1 = 120000, B2 = 2370000 (P-1 stage 2)

B1 = 224438 (P-1 stage 1)

B1 = 149626 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

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

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-03-07T19:42:35+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