1949/04/01 by Atle Selberg · 7 citations
Mathematics · #History and Theory of Mathematics
paper · doi:10.2307/1969455
openalex publication_date 1949/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/05
From this formula there are several ways to deduce the prime-number theorem. The way I present ??2-4 of this paper, is chosen because it seems at the present to be the most direct and most elementary way.1 But for completeness it has to be mentioned that this was not my first proof. The original proof was in fact rather different, and made use of the following result by P. Erdos, that for an arbitrary, positive fixed number 6, there exist a K(a) > 0 and an xo = x(a) such that for x > xo, there are more than K(a) Xlog x primes in the interval from x to x + Ax. My first proof then ran as follows: Introducing the notations