Abstract:

A general theorem is introduced and proved, a special case of which is the prime number theorem (PNT). The main theorem proved in this article is the following: [image omitted], where F:  →  is analytic for all x ≥ 2, and the p's in the sum represent all primes p ≤ N. Since PNT is used to derive our generalization, we may say that PNT and our generalization are equivalent.

Keywords: prime number theorem (PNT); logarithmic integral; Maclaurin series; generalized prime number theorem

Document Type: Research article

DOI: 10.1080/00207390701867455