Three Theorems on modular sieves that suggest the Prime Difference is O(Number of primes < (p(n)^1/2))

Abstract

This 1964 paper developed as an off-shoot to the foundational query: Do we discover the natural numbers (Platonically), or do we construct them linguistically? The paper also assumes computational significance in the light of Agrawal, Kayal and Saxena's August 2000 paper, "PRIMES is in P", since both the TRIM and Compact Number Generating algorithms - each of which generates all the primes - are deterministic algorithms that run in polynomial time and suggest that the Prime Difference, d(n), is O(Number of primes < (p(n)^1/2)).