M2228137 Mersenne number exponent details

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M2228137

<<<

>>>

is 2 ^2228137 - 1

has 670737 decimal digits

takes 0.147 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	7060DE316680B9A5	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	13.3358	67.1642%	2000000	65000000	0.5179	7.6557%	13.8537	69.6780%	2.5138%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8698%	0.0191	63.1575%	1.0885%
GPU72	2⁶²	0.2757	64.5161%	11000	180000	0.0019	1.6311%	0.2777	65.0949%	0.5788%
Difference	+5	+13.0600	+2.6481%	+1989000	+64820000	+0.5160	+6.0246%	+13.5760	+4.5831%	+4.5831%

Known prime factors (1 factor, 95.2 bits, 0.00427346% 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
2228137	46091217221142676006942220303	29	95.218	10342994443596303999023 10342994443596303999023	2016-11-25	1	10342994443596303999023	5.022e+9	5.372e+13	1.003e+14

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	-	-	0.281%
2004-01-07T00:00:00	markr	v4_computers	30000	532500		-		-	-	0.005	-	-	1.441%
2011-01-16T03:39:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.603%
2012-01-07T09:07:00	Squeeky_Squirrel	P4_2600	150000	3262500		-		-	-	0.030	-	-	3.218%
2015-11-23T19:12:41	Alexander Dubrovin	Manual testing	1000000	6000000	6	-		-	-	0.121	-	-	4.585%
2015-11-24T16:05:50	Alexander Dubrovin	Manual testing	1000000	14000000	12	-		-	-	0.163	-	-	5.497%
2016-01-05T12:37:21	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.656%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:09	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.069	-	-
2009-01-11T01:50:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-20T05:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.441	-	-
2015-03-06T11:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.881	-	-
2015-03-06T11:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.677	-	-
2015-10-25T20:35:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.354	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.315 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.315 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.058
50000	5000000	46091217221142676006942220303	3	0.257

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-11T13:01:00	paulie	iMac3.4	50000	5000000						3	0.257
2009-12-22T01:05:00	SubPrime	abd0	50000	5000000						3	0.257
2011-09-29T20:06:00	Bud	annan	50000	5000000						3	0.257
2013-06-18T23:04:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-21T06:22:00	Jason U	Server7	50000	5000000						3	0.257
2016-01-29T07:17:36	Olivier Termolle	KULbook	50000	5000000						3	0.257
2016-03-19T06:19:21	Jason U	Server7	50000	5000000						3	0.257
2016-07-09T23:32:10	Bruce	Desk6	50000	5000000						3	0.257
2016-11-25T20:15:27	Bruce	Desk6	50000	5000000	46091217221142676006942220303	95.218	3	2		3	0.257

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	7060DE316680B9A5	0.147

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T22:29:00

Oliver Kruse

GTX-2

46091217221142676006942220303

530A5B99886969__

2017-11-20T11:37:07

kkmrkkblmbrbk

c4.xlarge

46091217221142676006942220303

530A5B99886969__

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 = 14000000 (P-1 stage 2)

B1 = 1000000, B2 = 6000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 150000, B2 = 3262500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 30000, B2 = 532500 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

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TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-11-20T11:37:07+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