M2213923 Mersenne number exponent details

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M2213923

<<<

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is 2 ^2213923 - 1

has 666458 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	56195907D96C365C	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	13.4214	67.1642%	2000000	65000000	0.5179	7.6507%	13.9393	69.6764%	2.5122%
PrimeNet	2⁵⁸	0.0173	62.0690%	10000	180000	0.0018	2.8664%	0.0192	63.1562%	1.0873%
GPU72	2⁶²	0.2775	64.5161%	11000	170000	0.0019	1.6020%	0.2794	65.0846%	0.5685%
Difference	+5	+13.1439	+2.6481%	+1989000	+64830000	+0.5160	+6.0487%	+13.6599	+4.5918%	+4.5918%

Known prime factors (1 factor, 109.0 bits, 0.00492520% 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
2213923	667391587216158093790340977871399	33	109.040	150726016039437255448888913 7 × 21532288005633893635555559	2016-03-24	7	21532288005633893635555559	6.849e+10	1.118e+17	2.089e+17

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	-	-	0.281%
2010-10-10T19:58:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.781%
2010-12-01T17:23:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.456%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	113991	113991		-		-	-	0.011	-	-	0.999%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	142982	142982		-		-	-	0.014	-	-	1.131%
2015-04-26T13:52:00	Squeeky_Squirrel	P4_2600	160000	4600000		-		-	-	0.038	-	-	3.500%
2015-11-14T20:39:29	Alexander Dubrovin	Manual testing	1000000	5000000	6	-		-	-	0.116	-	-	4.388%
2015-11-14T20:39:29	Alexander Dubrovin	Manual testing	1500000	10000000	12	-		-	-	0.187	-	-	5.282%
2015-12-11T13:23:51	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.651%
2016-04-23T18:02:03	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.186%

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	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-07T18:27:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-18T05:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.139	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.443	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.887	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.688	-	-
2015-10-22T10:17:22	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.375	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.714 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	1.714 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.542
50000	5000000	667391587216158093790340977871399	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-09T11:29:00	Smurgs	Praca	50000	5000000						3	0.257
2009-12-16T04:42:00	James Classen	towerofart	50000	5000000						3	0.257
2011-09-16T14:05:00	Bud	annan	50000	5000000						3	0.257
2011-09-21T06:30:00	Bud	annan	50000	5000000						3	0.257
2015-03-16T02:18:00	Bruce	desk16	50000	5000000						3	0.257
2016-03-15T05:50:15	Jason U	Server7	50000	5000000						3	0.257
2016-03-24T21:39:31	Bruce	Desk6	50000	5000000	667391587216158093790340977871399	109.040	2	2		2	0.171

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	4A89359D3ADFFF__	0.146
1999-08-07T00:00:00	ANONYMOUS	v4_computers	56195907D96C365C	0.146

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T18:19:15

Oliver Kruse

GTX-3

667391587216158093790340977871399

FCBCF79510B1CA__

2017-11-20T07:47:47

kkmrkkblmbrbk

c4.xlarge

667391587216158093790340977871399

FCBCF79510B1CA__

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 = 1500000, B2 = 10000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

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

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (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 = 142982 (P-1 stage 1)

B1 = 113991 (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)

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TF factor-bounds graph:

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Last modified: 2017-11-20T07:47:47+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