Sierpinskin luku Sisällysluettelo Sierpinskin ongelma | Katso myös | Lähteet | Aiheesta muualla | NavigointivalikkoSeventeen or Bust: Project statsSeventeen or Bustlaajentamalla

LukuteoriaRatkaisemattomat matemaattiset ongelmat


Lukuteoriassaparitontaluonnollista lukuakokonaisluvutyhdistettyjä lukujaalkulukujaProthin luvuiksi1960Wacław Sierpiński1962John SelfridgeSeventeen or Bust





Lukuteoriassa Sierpinskin luku tarkoittaa sellaista paritonta luonnollista lukua k, jolle pätee, että kaikki kokonaisluvut muotoa k × 2n + 1 ovat yhdistettyjä lukuja (siis eivät ole alkulukuja) kaikilla n:n arvoilla.


Toisin sanoen k:n ollessa Sierpinskin luku kaikki joukon


k⋅2n+1:n∈Ndisplaystyle left,kcdot 2^n+1:nin mathbb N ,right

alkiot ovat yhdistettyjä lukuja. Joukon lukuja, kun k on pariton ja k<2ndisplaystyle k<2^n, kutsutaan Prothin luvuiksi.


Vuonna 1960 Wacław Sierpiński, jonka mukaan Sierpinskin luku on nimetty, todisti, että on olemassa äärettömän monta paritonta kokonaislukua k, jotka eivät tuota alkulukuja.




Sisällysluettelo





  • 1 Sierpinskin ongelma


  • 2 Katso myös


  • 3 Lähteet


  • 4 Aiheesta muualla




Sierpinskin ongelma |


Sierpinskin ongelma kysyy, mikä on pienin Sierpinskin luku. Vuonna 1962[1]John Selfridge todisti, että 78 557 on Sierpinskin luku. Hän julkisti (mutta ei todistanut) Selfridgen konjektuurin, jonka mukaan 78 557 olisi pienin Sierpinskin luku ja siten siis vastaus Sierpinskin ongelmaan. Internetissä toimiva hajautetun laskennan projekti Seventeen or Bust etsii pienintä mahdollista Sierpinskin lukua ja pyrkii todistamaan Sierpinskin ongelmaa. Lokakuussa 2009 on jäljellä enää kuusi ehdokasta mahdollisiksi 78 557:ää pienemmiksi Sierpinskin luvuiksi: 10 223, 21 181, 22 699, 24 737, 55 459 ja 67 607.[2]



Katso myös |


  • Brierin luku


Lähteet |



  1. ↑ bit.ly/Xt3S9Y John Selfridge


  2. ↑ Seventeen or Bust: Project stats



Aiheesta muualla |


  • Seventeen or Bust

Käännös suomeksi
Tämä artikkeli tai sen osa on käännetty tai siihen on haettu tietoja muunkielisen Wikipedian artikkelista.
Alkuperäinen artikkeli: en:Sierpinski number



Tämä matematiikkaan liittyvä artikkeli on tynkä. Voit auttaa Wikipediaa laajentamalla artikkelia.






-

Popular posts from this blog

Is there a general name for the setup in which payoffs are not known exactly but players try to influence each other's perception of the payoffs?Osborne, Nash equilibria and the correctness of beliefsIs there a name for this family of games (Binomial games?)?Perfect Bayesian EquilibriumCalculating mixed strategy equilibrium in battle of sexesPure Strategy SPNEIs there a commitment mechanism which allows players to achieve pareto optimal solutions?Extensive Form GamesAn $n$-player prisoner's dilemma where a coalition of 2 players is better off defectingTit-For-Stat Strategy Best RepliesPotential solutions of the $n$-player Prisoner's Dilemma

Image
Decoupling cap routing on a 4 layer PCB Which module had more 'comfort' in terms of living space, the Lunar Module or the Command module? Why do only some White Walkers shatter into ice chips? What are the advantages of luxury car brands like Acura/Lexus over their sibling non-luxury brands Honda/Toyota? I have a unique character that I'm having a problem writing. He's a virus! exec command in bash loop Can my company stop me from working overtime? Pressure inside an infinite ocean? PN junction band gap - equal across all devices? I'm in your subnets, golfing your code How long would it take for people to notice a mass disappearance? Will 700 more planes a day fly because of the Heathrow expansion? Introducing Gladys, an intrepid globetrotter What matters more when it comes to book covers? Is it ‘professional quality’ or relevancy? What is the most remote airport from the center of the city it supposedly serves? How do LIGO and VIRGO kn...
Read more

Is flight data recorder erased after every flight?When are black boxes used?What protects the location beacon (pinger) of a flight data recorder?Is there anywhere I can pick up raw flight data recorder information?Who legally owns the Flight Data Recorder?Constructing flight recorder dataWhy are FDRs and CVRs still two separate physical devices?What are the data elements shown on the GE235 flight data recorder (FDR) plot?Are CVR and FDR reset after every flight?What is the format of data stored by a Flight Data Recorder?How much data is stored in the flight data recorder per hour in a typical flight of an A380?Is a smart flight data recorder possible?

Image
Why are prions in animal diets not destroyed by the digestive system? How to increase the size of the cursor in Lubuntu 19.04? As matter approaches a black hole, does it speed up? Why is B♯ higher than C♭ in 31-ET? Nominativ or Akkusativ What does this colon mean? It is not labeling, it is not ternary operator Didn't attend field-specific conferences during my PhD; how much of a disadvantage is it? Applying a GPO to local users except local administrators on Workgroup computers Why has the UK chosen to use Huawei infrastructure when Five Eyes allies haven't? Using column size much larger than necessary Can my company stop me from working overtime? Will 700 more planes a day fly because of the Heathrow expansion? How to use dependency injection and avoid temporal coupling? Point of the Dothraki's attack in GoT S8E3? How I can I roll a number of non-digital dice to get a random number between 1 and 150? Validation rule Scheduled Apex I need a d...
Read more

Rank groups within a grouped sequence of TRUE/FALSE and NAGrouping functions (tapply, by, aggregate) and the *apply familyCharacters counting and subletting specific patternsWhat is the purpose of setting a key in data.table?data.table vs dplyr: can one do something well the other can't or does poorly?how to make a bar plot for a list of dataframes?How to group by unique values in a list in RPandas - Alternative to rank() function that gives unique ordinal ranks for a columnRank within group in for loop in RData transformation: from dyadic to observational data in RGetting map from purrr to work with paste0

Image
Understanding trademark infringements in a world where many dictionary words are trademarks? How to use dependency injection and avoid temporal coupling? How to write a 12-bar blues melody Can you Ready a Bard spell to release it after using Battle Magic? Why did the Apollo 13 crew extend the LM landing gear? SafeCracker #3 - We've Been Blocked As a Bard multi-classing into Warlock, what spells do I get? Multiple SQL versions with Docker Didn't attend field-specific conferences during my PhD; how much of a disadvantage is it? Copy previous line to current line from text file Would glacier 'trees' be plausible? As matter approaches a black hole, does it speed up? Find the cheapest shipping option based on item weight Python - What if the end-user didn't have the required library? Why does this derived table improve performance? Appropriate certificate to ask for a fibre installation (ANSI/TIA-568.3-D?) How can internet speed be 10 time...
Read more