M2163349 Mersenne number exponent details

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M2163349

<<<

>>>

is 2 ^2163349 - 1

has 651233 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	124D3A167164E4B3	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	2⁶⁸	27.5521	67.6471%	5000000	200000000	1.4896	8.9431%	29.0417	70.5404%	2.8933%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8542%	0.0196	63.1516%	1.0826%
GPU72	2⁶²	0.2840	64.5161%	10000	160000	0.0017	1.5197%	0.2857	65.0554%	0.5393%
Difference	+6	+27.2681	+3.1309%	+4990000	+199840000	+1.4878	+7.4233%	+28.7560	+5.4850%	+5.4850%

Known prime factors (1 factor, 71.9 bits, 0.00332327% 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
2163349	4387582480384700959471	22	71.894	1014071811895515 3 × 5 × 67 × 317 × 3183049459	2020-01-28	317	3183049459	408.33	16.534	30.880

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	-	-	0.225%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-07T03:25:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.354%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.513%
2011-01-22T10:46:00	markr	tiny	120000	2340000		-		-	-	0.023	-	-	2.547%
2014-10-05T22:22:00	Jocelyn Larouche	Manual testing	149669	149669		-		-	-	0.014	-	-	1.008%
2016-04-20T21:55:08	Jocelyn Larouche	Manual testing	240000	8835230	12	-		-	-	0.068	-	-	3.823%
2017-09-05T23:15:04	Jocelyn Larouche	low 4M	480000	4800000	6	-		-	-	0.068	-	-	3.683%
2017-09-13T23:12:01	Jocelyn Larouche	low 4M	576000	5760000	6	-		-	-	0.082	-	-	3.915%
2019-10-21T02:21:30	mikr	MSI	5000000	200000000	12	-		-	-	1.490	-	-	8.943%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T17:35:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-07T11:29:00	Sturle Sunde	goscha.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.454	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.908	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.727	-	-
2015-12-30T18:01:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.454	-	-
2016-11-11T01:20:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.908	-	-
2019-05-13T13:38:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.82	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.759 GHz-days
Estimated T-Level:	2.200

Digits	B1	Curves	Complete	FacMiss
20	11000	44 / 100	0.440	64.261%
25	50000	44 / 280	0.157	85.434%

New Calculation Method

Total ECM effort:	3.759 GHz-days
Estimated T-Level:	2.200

Digits	B1	Complete	FacMiss
20	11000	1.419	24.187%
25	50000	0.128	87.961%
30	250000	0.008	99.213%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		42	3.588
50000	5000000	4387582480384700959471	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-19T03:05:00	Smurgs	Praca	50000	5000000						3	0.256
2009-12-01T17:23:00	SubPrime	mysql0	50000	5000000						3	0.256
2011-10-21T12:22:00	Bud	annan	50000	5000000						3	0.256
2013-05-03T13:46:00	Xyzzy	J	50000	5000000						3	0.256
2015-01-30T15:31:00	OS1	L3	50000	5000000						3	0.256
2015-09-24T17:13:59	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2016-03-01T21:46:16	arnaud	CHAMOT09	50000	5000000						3	0.256
2016-06-20T05:05:43	Bruce	test	50000	5000000						3	0.256
2016-10-08T23:52:14	Bruce	Desk6	50000	5000000						3	0.256
2017-03-26T09:53:42	Bruce	Desk6	50000	5000000						3	0.256
2017-10-21T02:47:38	Conductor	Sasha	50000	5000000						3	0.256
2018-02-27T17:37:38	Bruce	Desk6	50000	5000000						3	0.256
2018-08-09T10:52:04	-Anonymous-	Kitchen	50000	5000000						3	0.256
2019-11-10T02:33:15	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-28T07:11:41	Keysarecool	Boat_Anchor	50000	5000000	4387582480384700959471	71.894	2	2	5657159467464398	2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-17T00:00:00	ANONYMOUS	v4_computers	124D3A167164E4B3	0.142
1999-02-07T00:00:00	ANONYMOUS	v4_computers	124D3A167164E4B3	0.142
2018-04-11T03:06:15	kkmrkkblmbrbk	old	124D3A167164E4B3	0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-01-29T00:50:14

Niels_Mache_Nextcloud

SuperDry-X

4387582480384700959471

44C144C45C76F371

2020-01-29T12:31:57

Jinyuan Wang

Manual testing

4387582480384700959471

44C144C45C76F371

2020-01-29T19:58:31

marssystems

SYSTEM01

4387582480384700959471

44C144C45C76F371

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 576000, B2 = 5760000 (P-1 stage 2)

B1 = 480000, B2 = 4800000 (P-1 stage 2)

B1 = 240000, B2 = 8835230 (P-1 stage 2)

B1 = 576000 (P-1 stage 1)

B1 = 480000 (P-1 stage 1)

B1 = 120000, B2 = 2340000 (P-1 stage 2)

B1 = 240000 (P-1 stage 1)

B1 = 149669 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-01-29T19:58:31+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