M2221229 Mersenne number exponent details

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M2221229

<<<

>>>

is 2 ^2221229 - 1

has 668657 decimal digits

takes 0.146 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	71F6E2779B19D8BD	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	26.8342	67.6471%	2000000	65000000	0.5179	7.0338%	27.3521	69.9227%	2.2756%
PrimeNet	2⁵⁸	0.0173	62.0690%	10000	180000	0.0018	2.8681%	0.0191	63.1569%	1.0879%
GPU72	2⁶²	0.2766	64.5161%	11000	180000	0.0019	1.6301%	0.2785	65.0945%	0.5784%
Difference	+6	+26.5576	+3.1309%	+1989000	+64820000	+0.5160	+5.4037%	+27.0736	+4.8282%	+4.8282%

Known prime factors (1 factor, 76.1 bits, 0.00342409% 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
2221229	78590620456788325809223	23	76.057	17690796504274959 3³ × 13 × 181 × 278459279789	2020-02-13	181	278459279789	7,216.5	1,446.4	2,701.4

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.227%
2010-10-13T16:44:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.674%
2011-01-01T18:25:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.176%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	113896	113896		-		-	-	0.011	-	-	0.868%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	142792	142792		-		-	-	0.014	-	-	0.987%
2015-05-01T01:56:00	Squeeky_Squirrel	P4_2600	160000	4600000		-		-	-	0.038	-	-	3.136%
2015-11-19T06:48:34	Alexander Dubrovin	Manual testing	1000000	5000000	6	-		-	-	0.116	-	-	3.983%
2015-11-19T06:48:35	Alexander Dubrovin	Manual testing	1000000	10000000	6	-		-	-	0.142	-	-	4.670%
2015-12-20T16:44:20	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.034%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:09	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-11T02:58:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-19T00:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-01-23T08:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.442	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.884	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.682	-	-
2015-10-23T09:34:54	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.364	-	-
2016-03-15T15:38:09	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	6.728	-	-
2019-04-22T13:11:39	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.46	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.514 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	3.514 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.323	26.645%
25	50000	0.120	88.733%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		40	3.429
50000	5000000	78590620456788325809223	1	0.086

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-22T21:26:00	mgsoft	casoria04	50000	5000000						3	0.257
2009-12-18T07:11:00	James Classen	towerofart	50000	5000000						3	0.257
2011-09-24T20:19:00	S36049	Wolle5	50000	5000000						3	0.257
2013-06-17T05:28:00	OS1	L3	50000	5000000						3	0.257
2015-03-18T02:18:00	Bruce	desk16	50000	5000000						3	0.257
2016-01-25T03:34:59	Jason U	Server7	50000	5000000						3	0.257
2016-03-17T05:52:36	Bruce	Desk6	50000	5000000						3	0.257
2016-07-07T03:53:49	lettp	Home	50000	5000000						3	0.257
2016-11-20T11:55:12	NBCC		50000	5000000						3	0.257
2017-01-24T23:30:15	Alexander Dubrovin	Manual testing	50000	5000000						1	0.086
2017-08-07T07:37:40	Bruce	Desk6	50000	5000000						3	0.257
2018-01-04T07:43:11	Bruce	Desk6	50000	5000000						3	0.257
2018-06-24T14:03:41	Bruce	Desk6	50000	5000000						3	0.257
2019-07-28T09:15:17	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-02-13T21:21:51	mnd9	office2	50000	5000000	78590620456788325809223	76.057	1	2	2548890995973195	1	0.086

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	71F6E2779B19D8BD	0.146
2018-04-19T01:07:55	kkmrkkblmbrbk	old	71F6E2779B19D8BD	0.146

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-02-14T09:21:02

Jinyuan Wang

Manual testing

78590620456788325809223

A1C06329E81DD0B8

2020-02-16T14:52:44

Bommer

2600X

78590620456788325809223

A1C06329E81DD0B8

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 = 2000000, B2 = 65000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1000000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000, B2 = 5000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 160000, B2 = 4600000 (P-1 stage 2)

B1 = 85000, B2 = 1593750 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 142792 (P-1 stage 1)

B1 = 113896 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (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

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-02-16T14:52:44+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