M3394487 Mersenne number exponent details

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M3394487

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>>>

is 2 ^3394487 - 1

has 1021843 decimal digits

takes 0.357 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	6CBC72F7CEB572A3	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	35.1708	68.1159%	4000000	150000000	1.8206	8.1448%	36.9913	70.7128%	2.5969%
PrimeNet	2⁶⁰	0.0452	63.3333%	14000	280000	0.0043	2.8464%	0.0496	64.3770%	1.0437%
GPU72	2⁶⁴	1.0486	65.6250%	18000	320000	0.0052	1.7915%	1.0538	66.2408%	0.6158%
Difference	+5	+34.1222	+2.4909%	+3982000	+149680000	+1.8153	+6.3533%	+35.9375	+4.4720%	+4.4720%

Known prime factors (1 factor, 98.2 bits, 0.00289339% 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
3394487	368037528435456344101405085743	30	98.216	54211067598057724790433 3² × 59 × 1567 × 8573 × 59557 × 127602389	2021-07-15	59557	127602389	3.403e+10	1.0673	1.9774

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-15T21:07:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.693%
2011-10-24T00:50:00	harlee	P4_2600	60000	945000		-		-	-	0.016	-	-	1.661%
2014-07-04T02:22:00	Jocelyn Larouche	Manual testing	78908	78908		-		-	-	0.012	-	-	0.652%
2014-10-13T22:29:00	Jocelyn Larouche	Manual testing	97816	97816		-		-	-	0.015	-	-	0.745%
2015-09-18T18:59:00	Jocelyn Larouche	Manual testing	422183	422183		-		-	-	0.064	-	-	1.605%
2015-11-21T13:57:56	Jocelyn Larouche	Manual testing	532334	532334		-		-	-	0.081	-	-	1.779%
2016-03-10T11:59:59	Jocelyn Larouche	Manual testing	638800	11498400	6	-		-	-	0.187	-	-	4.397%
2021-07-15T01:56:36	mikr	MSI	4000000	150000000	12		368037528435456344101405085743	30	98.216	1.821	0.713	3.641	8.145%
2022-03-16T19:11:55	Jocelyn Larouche	Manual testing	1000000	127313550		-		-	-	1.200	-	-	6.988%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:27	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.045	-	-
2009-03-25T05:54:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-20T05:42:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.090	-	-
2012-11-15T00:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.470	-	-
2016-02-23T16:29:27	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.289	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.578	-	-
2015-02-18T11:36:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.101	-	-
2015-04-04T13:44:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.201	-	-
2017-03-12T14:28:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.403	-	-
2018-09-10T13:18:22	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.806	-	-
2021-06-21T08:52:57	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	17.61	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.301 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	6.301 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.387	24.980%
25	50000	0.125	88.218%
30	250000	0.008	99.231%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	6.301

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-03T22:07:00	Aca Arsov	backo6400	50000	5000000						3	0.440
2011-12-20T04:16:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.440
2014-11-12T10:26:00	Lukasz Wrobel	i-5	50000	5000000						3	0.440
2016-11-21T15:23:46	f0rteOC	Fortissimo	50000	5000000						3	0.440
2019-04-23T10:34:04	Idgo	Pentium_Desktop	50000	5000000						3	0.440
2021-03-01T22:55:04	mnd9	50869	50000	5000000						7	1.026
2021-05-28T08:28:33	IanGlencross	glenx24	50000	5000000						7	1.026
2021-06-04T11:47:44	LordJulius	Ev	50000	5000000						7	1.026
2021-07-05T17:18:59	RIHATEC	i7-3770K	50000	5000000						7	1.026

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	F0D1D3C773D22A__	0.357

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-07-15T08:41:29

SRJ2877

LTOS

368037528435456344101405085743

6CBC72F7CEB572A3

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 127313550 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 638800, B2 = 11498400 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 638800 (P-1 stage 1)

B1 = 532334 (P-1 stage 1)

B1 = 422183 (P-1 stage 1)

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

B1 = 97816 (P-1 stage 1)

B1 = 78908 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-16T19:11:55+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