M3383431 Mersenne number exponent details

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M3383431

<<<

>>>

is 2 ^3383431 - 1

has 1018515 decimal digits

takes 0.355 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	B734898D20AE6F1C	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	2⁶⁸	17.6167	67.6471%	4000000	150000000	1.8206	8.8071%	19.4372	70.4964%	2.8494%
PrimeNet	2⁶⁰	0.0454	63.3333%	14000	280000	0.0043	2.8447%	0.0497	64.3764%	1.0431%
GPU72	2⁶⁴	1.0520	65.6250%	18000	320000	0.0052	1.7904%	1.0572	66.2404%	0.6154%
Difference	+4	+16.5647	+2.0221%	+3982000	+149680000	+1.8153	+7.0167%	+18.3800	+4.2560%	+4.2560%

Known prime factors (1 factor, 109.3 bits, 0.00323132% 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
3383431	815604249170138326729065755452423	33	109.330	120529168345702679724969381 3⁴ × 7 × 211 × 269 × 157327 × 1864853 × 12765167	2021-05-08	1864853	12765167	5.010e+10	0.3744	0.5780

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-10T06:10:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.811%
2011-10-21T03:07:00	harlee	P4_2600	60000	930000		-		-	-	0.016	-	-	1.881%
2014-07-04T02:22:00	Jocelyn Larouche	Manual testing	78970	78970		-		-	-	0.012	-	-	0.755%
2014-10-12T23:58:00	Jocelyn Larouche	Manual testing	97940	97940		-		-	-	0.015	-	-	0.860%
2015-08-13T18:13:00	Squeeky_Squirrel	P4_2600	165000	4372500		-		-	-	0.060	-	-	3.309%
2017-04-18T12:05:01	Jocelyn Larouche	low 4M	330000	3300000	6	-		-	-	0.075	-	-	3.428%
2021-05-08T21:36:18	mikr	MSI	4000000	150000000	12		815604249170138326729065755452423	33	109.330	1.821	0.711	3.641	8.807%
2022-02-25T17:22:04	Jocelyn Larouche	Manual testing	200000	200000		-		-	-	0.030	-	-	1.270%
2022-04-09T09:24:10	Jocelyn Larouche	Manual testing	1000000	1000000		-		-	-	0.152	-	-	2.569%
2022-04-10T15:21:20	Jocelyn Larouche	Manual testing	1000000	126668850		-		-	-	1.195	-	-	7.611%

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	-	-
2009-03-26T05:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-30T13:47:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.091	-	-
2012-11-15T00:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.472	-	-
2016-02-23T16:29:27	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.290	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.580	-	-
2015-02-15T12:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.104	-	-
2015-04-01T23:42:00	Gordon Spence	Manual testing	2⁶⁵	2⁶⁶		-	-	2.209	-	-
2017-03-10T14:13:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.417	-	-
2018-10-08T14:27:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.835	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.247 GHz-days
Estimated T-Level:	1.450

Digits	B1	Curves	Complete	FacMiss
20	11000	29 / 100	0.290	74.717%
25	50000	29 / 280	0.104	90.144%

New Calculation Method

Total ECM effort:	4.247 GHz-days
Estimated T-Level:	1.450

Digits	B1	Complete	FacMiss
20	11000	0.935	39.240%
25	50000	0.085	91.893%
30	250000	0.005	99.481%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	4.247

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-13T21:34:00	Net_Force	Vista64	50000	5000000						3	0.439
2011-12-23T06:28:00	schelle	video	50000	5000000						3	0.439
2014-10-20T13:18:00	arnaud	Chamot18	50000	5000000						3	0.439
2016-11-13T17:48:03	Dennis Schreiber	z400	50000	5000000						3	0.439
2019-04-17T23:17:00	furkell	furkell1	50000	5000000						3	0.439
2021-02-26T00:24:39	MarkS	desktop-i7	50000	5000000						7	1.025
2021-03-30T20:57:11	Zenzoma	AMD3970X	50000	5000000						7	1.025

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	ANONYMOUS	v4_computers	485B7317A2AC1E__	0.355

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-09T02:18:33

mikr

Nitron

815604249170138326729065755452423

B734898D20AE6F1C

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 = 126668850 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 330000, B2 = 3300000 (P-1 stage 2)

B1 = 165000, B2 = 4372500 (P-1 stage 2)

B1 = 330000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

B1 = 60000, B2 = 930000 (P-1 stage 2)

B1 = 97940 (P-1 stage 1)

B1 = 78970 (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:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-04-10T15:21:20+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