The prime power conjecture is true for $n < 2{,}000{,}000$

Abstract

The Prime Power Conjecture (PPC) states that abelian planar difference sets of order $n$ exist only for $n$ a prime power. Evans and Mann verified this for cyclic difference sets for $n \leq 1600$. In this paper we verify the PPC for $n \leq 2{,}000{,}000$, using many necessary conditions on the group of multipliers.