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

[[Himpunan (matematika)|Himpunan]] dari semua bilangan prima terkadang dilambangkan dengan <math>\mathbf{P}</math> (dengan [[huruf tebal]] kapital ''P'')<ref>{{cite book|title=Elementary Methods in Number Theory|volume=195|series=Graduate Texts in Mathematics|contribution=Notations and Conventions|contribution-url=https://books.google.com/books?id=sE7lBwAAQBAJ&pg=PP10|first=Melvyn B.|last=Nathanson|author-link=Melvyn B. Nathanson|publisher=Springer|year=2000|isbn=978-0-387-22738-2|mr=1732941}}</ref> atau dengan <math>\mathbb{P}</math> (dengan [[papan tulis tebal]] kapital P).<ref>{{cite book|title=The Mathematics of Infinity: A Guide to Great Ideas|volume=111|series=Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts|first=Theodore G.|last=Faticoni|edition=2nd|publisher=John Wiley & Sons|year=2012|isbn=978-1-118-24382-4|page=44|url=https://books.google.com/books?id=I433i_ZGxRsC&pg=PA44}}</ref>

 

 

The [[Rhind Mathematical Papyrus]], from around 1550 BC, has [[Egyptian fraction]] expansions of different forms for prime and composite numbers.<ref>Bruins, Evert Marie, review in ''Mathematical Reviews'' of {{cite journal | last = Gillings | first = R.J. | doi = 10.1007/BF01307175 | journal = Archive for History of Exact Sciences | mr = 0497458 | pages = 291–298 | title = The recto of the Rhind Mathematical Papyrus. How did the ancient Egyptian scribe prepare it? | volume = 12 | issue = 4 | year = 1974| s2cid = 121046003 }}</ref> However, the earliest surviving records of the explicit study of prime numbers come from [[Greek mathematics|ancient Greek mathematics]]. [[Euclid]]'s ''[[Euclid's Elements|Elements]]'' (c. 300 BC) proves the [[infinitude of primes]] and the [[fundamental theorem of arithmetic]], and shows how to construct a [[perfect number]] from a [[Mersenne prime]].<ref name="stillwell-2010-p40">{{cite book|title=Mathematics and Its History|series=Undergraduate Texts in Mathematics|first=John|last=Stillwell|author-link=John Stillwell|edition=3rd|publisher=Springer|year=2010|isbn=978-1-4419-6052-8|page=40|url=https://books.google.com/books?id=V7mxZqjs5yUC&pg=PA40}}</ref> Another Greek invention, the [[Sieve of Eratosthenes]], is still used to construct lists of primes.<ref name="pomerance-sciam">{{cite journal|title=The Search for Prime Numbers|first=Carl|last=Pomerance|author-link=Carl Pomerance|journal=[[Scientific American]]|volume=247|issue=6|date=December 1982|pages=136–147|jstor=24966751|doi=10.1038/scientificamerican1282-136|bibcode=1982SciAm.247f.136P}}</ref><ref name="mollin">{{cite journal | last = Mollin | first = Richard A. | doi = 10.2307/3219180 | issue = 1 | journal = Mathematics Magazine | mr = 2107288 | pages = 18–29 | title = A brief history of factoring and primality testing B. C. (before computers) | volume = 75 | year = 2002| jstor = 3219180 }}</ref>