Conjecture: the Set of Prime Numbers Is Supernatural

Abstract

Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlightening us about their repartition, the set of prime numbers is often informally qualified as mysterious. In the present paper, we introduce a formalism allowing to state a formal conjecture: the set of prime numbers is supernatural. Our conjecture has no analogue in the existing literature. This conjecture is expected to be a hard challenge for any kind of intelligence. We also find a Fermat-like function giving more prime numbers than Fermat's function.