Formulae for the nth Prime

Abstract

The present paper arose out of an attempt to answer the classical questions raised in [1] about formulae for the rath prime pn. Here are obtained a number of recurrence formulae for p_n as a symmetric function of the primes p₁, p₂, ..., p_n-1. Also the existence of rational algebraic functions in n arguments, such that the limit of the ratio of their logarithms gives p_n, is established. In [2], Isenkrahe has given a more complicated expression for p_n in terms of the previous primes, but there is nothing in common, either in content or method, between his work and the present one.