A property of the sequence of primes (Q1100502)

A sequence \((a_ n)\) of integers is called k-periodic (k\(\in {\mathbb{N}})\), if there are positive integers \(\ell\) and \(n_ 0\), so that for \(n\geq n_ 0\), \(a_{n+\ell}\equiv a_ n mod k\). By analytical means, but without using Turán's power sum method, it is shown that the series of primes (in natural order) is non k-periodic for all \(k>2\).