Pengguna:Klasüo/bak pasir/khusus/1: Perbedaan antara revisi

===FormulasRumus forbilangan primesprima===

{{main|FormulaRumus forbilangan primesprima}}

ThereTidak isada norumus knownefisien efficientyang formuladiketahui foruntuk primesbilangan prima. For exampleMisalnya, theretidak is no non-constantada [[polynomialpolinomial]] non-konstan, evenbahkan indalam several variables,beberapa thatvariabel takesmengambil ''onlyhanya'' primebilangan valuesprima.<ref name="matiyasevich"/> HoweverNamun, thereada arebanyak numerousekspresi expressionsyang thatmengkodekan dosemua encodebilangan allprima primes,atau orhanya onlybilangan primesprima. OneSatu possiblerumus formulayang ismungkin baseddidasarkan onpada [[teorema Wilson's theorem]] anddan generatesmenghasilkan the numberangka 2 many timesberkali-kali anddan allsemua otherbilangan primesprima exactlylainnya oncetepat.<ref>{{cite journal | last = Mackinnon | first = Nick | date = June 1987 | doi = 10.2307/3616496 | issue = 456 | pages = 113–114 | journal = [[The Mathematical Gazette]] | title = Prime number formulae | volume = 71| jstor = 3616496 }}</ref> ThereAda ispula alsosatu a set ofhimpunan [[persamaan Diophantine equations]] indalam ninesembilan variablesvariabel anddan onesatu parameter withdengan thesifat following propertyberikut: the parameter isbilangan primeprima ifjika anddan onlyhanya ifjika thesistem resultingpersamaan systemyang ofdihasilkan equationsmemiliki hassolusi aatas solutionbilangan over the natural numbersasli. ThisHal canini bedigunakan useduntuk tomendapatkan obtainrumus atunggal singledengan formulasifat withbahwa thesemua propertynilai that all its ''positive'' values"positif" areadalah primeprima.<ref name="matiyasevich">{{cite book | last = Matiyasevich | first = Yuri V. | author-link = Yuri Matiyasevich | year=1999 | chapter = Formulas for prime numbers | chapter-url=https://books.google.com/books?id=oLKlk5o6WroC&pg=PA13 | editor1-first=Serge | editor1-last = Tabachnikov | editor-link1=Sergei Tabachnikov| title = Kvant Selecta: Algebra and Analysis | volume = II | publisher = [[American Mathematical Society]] | isbn = 978-0-8218-1915-9 | pages=13–24}}</ref>

OtherContoh exampleslain ofdari primerumus pembangkit-generatingprima formulasberasal come fromdari [[teorema Mills' theorem]] and a theoremdan ofteorema [[E. M. Wright|Wright]]. Maka Theseini assertmenegaskan thatbahwa thereterdapat arekonstanta real constants <math>A>1</math> anddan <math>\mu</math> suchsedemikian rupa, thatsehingga

:<math>\left \lfloor A^{3^n}\right \rfloor \text{ anddan } \left \lfloor 2^{\cdots^{2^{2^\mu}}} \right \rfloor</math>

areadalah primeprima foruntuk anysembarang naturalbilangan numberasli <math>n</math> indalam the firstrumus formulapertama, anddan anysembarang numberbilangan ofeksponen exponentsdalam inrumus the second formulakedua.<ref>{{cite journal |first=E.M. |last= Wright | author-link=E. M. Wright |title=A prime-representing function |journal=[[American Mathematical Monthly]] |volume=58 |issue=9 |year=1951 |pages=616–618 |jstor=2306356 |doi= 10.2307/2306356}}</ref> HereSehingga <math>\lfloor {}\cdot{} \rfloor</math> represents themewakili [[floorfungsi functionlantai]], thebilangan largestbulat integerterbesar lessyang thankurang ordari equalatau tosama thedengan numberbilangan inyang questiondimaksud. HoweverNamun, thesehal areini notjustru usefultidak forberguna generatinguntuk primes,menghasilkan asbilangan theprima, primeskarena mustbilangan be generated firstprima inharus orderdibangkitkan toterlebih computedahulu theuntuk valuesmenghitung ofnilai <math>A</math> oratau <math>\mu.</math><ref name="matiyasevich"/>