An arithmetic term for the factorial function

Abstract

As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.

Keywords

• Elementary function
• Fermat number
• Kalmar function
• Prime-generating function
• Wilson’s theorem