https://www.maths.de/mde/information/landkarte/numbers/primzahlen.html
How can systematic any Primzahlen find?
the bekannteste take action is the Sieb the Eratosthenes, benannt to the greek Mathematiker Eratosthenes of Kyrene, the in the third vorchristlichen centenary lived. here his suggestion, circa any Primzahlen to find:
write The natural numbers, beginnend with 2, one after another there: 2, 3, 4, 5, 6, 7, 8, 9, ... Streiche any real Vielfachen of 2, means 4, 6, ...: 2, 3, 4, 5, 6, 7, 8, 9, ... Streiche any real Vielfachen of 3, means 6, 9, ... (The 6 is already in the first round ausgeschieden): 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
an so on: as nächstes go The Vielfachen of 5 gestrichen, then The of 7 etc. Accurate: in the k-ten Passage streiche The Vielfachen the k-ten number, The by then yet ,,survive hat; this is then The k-th Primzahl.
The Begründung for success the Verfahrens is easy: Each not-Primzahl n has a real Primteiler p, and so becomes n with the To p gehörigen Streichungsrunde gestrichen. |