M3426277 Mersenne number exponent details

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M3426277

<<<

>>>

is 2 ^3426277 - 1

has 1031413 decimal digits

takes 0.360 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	-unknown-	-unknown-
PRP	54652584B1A905F1	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	34.8445	68.1159%	14000000	700000000	7.8239	10.9059%	42.6684	71.5932%	3.4773%
PrimeNet	2⁶⁰	0.0448	63.3333%	14000	280000	0.0043	2.8511%	0.0492	64.3787%	1.0454%
GPU72	2⁶⁴	1.0388	65.6250%	19000	320000	0.0054	1.8218%	1.0442	66.2512%	0.6262%
Difference	+5	+33.8056	+2.4909%	+13981000	+699680000	+7.8185	+9.0842%	+41.6242	+5.3420%	+5.3420%

Known prime factors (1 factor, 69.5 bits, 0.00202940% 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
3426277	854039218606267770649	21	69.533	124630790010012 2² × 3³ × 11 × 13 × 8069851723	2021-05-01	27	8069851723	35.841	66.957	125.06

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-16T03:22:00	Carsten Kossendey	durandal	15000	210000		-		-	-	0.004	-	-	0.698%
2011-10-30T11:15:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.663%
2014-07-18T01:20:00	Jocelyn Larouche	Manual testing	78733	78733		-		-	-	0.012	-	-	0.652%
2014-09-13T17:15:00	HBendtz	HAL9007	500000	10000000		-		-	-	0.155	-	-	4.159%
2021-04-26T01:51:35	axn	Manual testing	14000000	700000000		-		-	-	7.824	-	-	10.906%
2022-04-09T09:24:22	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.308%
2022-04-10T15:21:26	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	6.989%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:29	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-24T06:24:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-07-24T20:25:00	Carsten Kossendey	Manual testing	2⁶¹	2⁶²		-	-	0.090	-	-
2012-08-18T15:31:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.466	-	-
2016-02-23T16:29:29	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.287	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.573	-	-
2015-02-07T18:04:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.091	-	-
2015-04-11T21:17:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.181	-	-
2017-02-05T22:59:56	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.362	-	-
2018-11-12T14:47:32	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.724	-	-
2020-12-30T17:06:32	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.45	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.964 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:	3.964 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		22	3.230
50000	5000000	854039218606267770649	5	0.734

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-04T12:02:00	Net_Force	Vista64	50000	5000000						3	0.440
2012-01-10T22:08:00	sannerud.com	Jens2010	50000	5000000						3	0.440
2015-01-02T09:09:00	joe b.	Pandora	50000	5000000						3	0.440
2016-12-10T15:22:56	Sid & Andy	Mrs_Potato_Head	50000	5000000						3	0.440
2019-05-22T06:01:10	Ondrej Vainlich	Intel_Corei5	50000	5000000						3	0.440
2021-03-19T13:14:26	Zenzoma	AMD3970X	50000	5000000						7	1.028
2021-05-01T10:17:09	daveward2005	Dave2	50000	5000000	854039218606267770649	69.533	5	2	3169253145599197	5	0.734

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-07T00:00:00	ANONYMOUS	v4_computers	D197FFF26C28A0__	0.360

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-01T10:49:48

ATH

ec2-PRPCF

854039218606267770649

54652584B1A905F1

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 = 14000000, B2 = 700000000 (P-1 stage 2)

B1 = 14000000 (P-1 stage 1)

B1 = 1000000, B2 = 126668850 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 60000, B2 = 945000 (P-1 stage 2)

B1 = 78733 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 210000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T15:21:26+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