Primes in Elliptic Divisibility Sequences

Abstract

Morgan Ward pursued the study of elliptic divisibility sequences, originally initiated by Lucas, and Chudnovsky and Chudnovsky subsequently suggested looking at elliptic divisibility sequences for prime appearance. The problem of prime appearance in these sequences is examined here, from both a theoretical and a practical viewpoint. We show calculations, together with a heuristic argument, to suggest that these sequences contain only finitely many primes.