M5393 Mersenne number exponent details

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M5393

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is 2 ⁵³⁹³ - 1

has 1624 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Last-known PrimeNet details:
-unknown- L-L tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	unknown			-	-	-	-	0.0000	0.0000%	-67.5000%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.5959%	0.0000	70.0959%	2.5959%
GPU72	2⁴⁴	0.0004	70.4545%	500	10000	0.0000	1.0433%	0.0004	71.4978%	1.0433%
Difference	-44	-0.0004	-70.4545%	-500	-10000	0.0000	-1.0433%	-0.0004	-71.4978%	-71.4978%

Known prime factors (4 factors, 5,393.0 bits, 100.00000000% known):

Remaining cofactor is a certified-prime

								GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
5393	32359	5	14.982	3 3	1	3	-	4.049e-13	1.019e-10	1.870e-10
5393	45252008098148953426302876081530345850393996751196 2417	54	178.240	41954392822314994832470680587363569303165211154456 2³ × 3² × 631 × 1879966351135060099 × 491208087342883430954335567	1879966351135060099	491208087342883430954335567	2021-04-07	3.024e+13	2.459e+15	4.592e+15
5393	12701337646329027207786029230875529620312749256224 07641153	58	189.695	11775762698246826634327859476057416670047051044153 6032 2⁵ × 191 × 30338770477745339 × 635049711900911930878017345654749	30338770477745339	635049711900911930878017345654749	2020-10-05	3.569e+13	3.179e+21	5.937e+21
5393	hide decimal representation P1509 click to show decimal representation	1,509	5,010.083				2021-04-07

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
5393	32359 45252008098148953426302876081530345850393996751196 2417	14643097300480019839217347671222404613728993408719 591851703	59	193.222
5393	32359 12701337646329027207786029230875529620312749256224 07641153	41100258489756099141674811988190126298370025318215 488860069927	62	204.677
5393	45252008098148953426302876081530345850393996751196 2417 12701337646329027207786029230875529620312749256224 07641153	57476103402900530694024613970920512244972670805449 10346599410455436271059616019684407883087303337072 74958546801	111	367.935
5393	32359 45252008098148953426302876081530345850393996751196 2417 12701337646329027207786029230875529620312749256224 07641153	18598692300144582727279424834850168557350706545935 27539056103229274622952181147809677546888220486843 3710383615933559	116	382.917

P-1 results:
Exponent "5393" not found

Trial Factoring results:
Exponent "5393" not found

ECM factoring results:

Total ECM effort:	23.367 GHz-days
Estimated T-Level:	33.513

Digits	B1	Curves	Complete	FacMiss
20	11000	1110 / 100	11.100	0.001%
25	50000	1110 / 280	3.964	1.885%
30	250000	1110 / 640	1.734	17.627%
35	1000000	1110 / 1580	0.703	49.522%
40	3000000	1110 / 4700	0.236	78.963%
45	11000000	220 / 9700	0.023	97.757%
50	44000000	202 / 17100	0.012	98.826%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		890	3.530
11000000	1100000000		18	0.262
44000000	4400000000		200	11.63
110000000	900514153782	45252008098148953426302876081530345850393996751196 2417	1	3.971
110000000	900514153782	12701337646329027207786029230875529620312749256224 07641153	1	3.971

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-21T07:51:00	unconnected	E5430-next	44000000	4400000000						200	11.63
2009-10-13T18:43:00	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2016-10-21T01:16:53	kkmrkkblmbrbk	old	3000000	300000000						889	3.526
2016-10-21T02:30:29	kkmrkkblmbrbk	old	11000000	1100000000						18	0.262
2020-10-05T20:28:26	Ryan Propper	Manual testing	110000000	900514153782	12701337646329027207786029230875529620312749256224 07641153	189.695	1	2	11360005842630690070	1	3.971
2021-04-07T13:56:11	Ryan Propper	Manual testing	110000000	900514153782	45252008098148953426302876081530345850393996751196 2417	178.240	1	2	4972235667295954912	1	3.971

Lucas-Lehmer results:
Exponent "5393" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:40:55

Oliver Kruse

Oliver-PC

32359

42A6ECF2D1C2AC__

2017-09-21T19:21:18

Oliver Kruse

Manual testing

32359

42A6ECF2D1C2AC__

2017-10-12T14:01:49

kkmrkkblmbrbk

Manual testing

32359

42A6ECF2D1C2AC__

2020-04-17T12:33:03

Oliver Kruse

IOS-1

32359

D8D8D893FE9771__

2020-10-05T20:38:17

firejuggler

Maison

32359

12701337646329027207786029230875529620312749256224
07641153

D8D8D893FE977173

2020-10-05T20:44:42

kotenok2000

shodan1

32359

12701337646329027207786029230875529620312749256224
07641153

D8D8D893FE977173

2021-04-07T16:27:33

mnd9

32359

45252008098148953426302876081530345850393996751196
2417

12701337646329027207786029230875529620312749256224
07641153

PRP

2021-04-10T02:39:03

Sébastien Broucke

Portable_Seb

32359

45252008098148953426302876081530345850393996751196
2417

12701337646329027207786029230875529620312749256224
07641153

PRP

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

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TF factor-bounds graph:

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2¹⁹⁰

Last modified: 2021-04-10T02:39:03+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