Abstract / résuméCUMC / CCEM 2005



Name / nom: Ryan Holm

School / école: University of Waterloo

Length / durée: 50 min

Title / titre: A Prime Number Between n and 2n: Erdos Betters Chebycheff and Ramanujan

Abstract / résumé: In 1845, Bertrand conjectured that there is always a prime number between n and 2n for any natural number n. In 1850, Chebycheff proved this conjecture and in 1919, Ramanujan discovered an even simpler proof. However, this proof was still quite involved. Then in 1932, Erdos discovered an even shorter, more elegant proof that involved nothing more than very elementary mathematics. In my talk I will put on display Erdos's beautiful proof as well as mention some generalizations and further results.

Prerequisites / choses nécessaires: There are virtually no prerequisites except for mathematical maturity, as Erdos's proof involves nothing much beyond the realm of high school mathematics.



PDF format / format PDF: holm.pdf