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Osječki matematički list, Vol. 17 No. 2, 2017.

Stručni rad

Bertrand’s postulate

Andrijana Ćurković orcid id orcid.org/0000-0003-2340-5767 ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu
Borka Jadrijević orcid id orcid.org/0000-0002-5913-3719 ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu
Marina Simić ; ∗Prirodoslovno-matematički fakultet, Sveučilište u Splitu

Puni tekst: hrvatski pdf 404 Kb

str. 139-150

preuzimanja: 555

citiraj

Sažetak

Joseph Bertrand, in 1845, conjectured that for all positive integers n there exists a prime number between n and 2n. This statement is known as Bertrand’s postulate. Bertrand verified his conjecture for n < \(3 · 10^{6}\) , but he did not prove it. The conjecture was proved in 1850 by Pafnuty Cherbyshev. In this paper we present the proof published by Paul Erdös in his first article in 1932. The proof is lementary and uses only a few simple properties of binomial coefficients. In addition, we will see how Bertrand’s postulate is related to some famous assertions and conjectures concerning prime numbers.

Ključne riječi

Bertrand’s postulate; prime numbers; binomial coefficient; Prime Number Theorem; Goldbach’s conjecture

Hrčak ID:

193190

URI

https://hrcak.srce.hr/193190

Datum izdavanja:

19.12.2017.

Podaci na drugim jezicima: hrvatski

Posjeta: 1.578 *