Author(s)

Pal Doroszlai, Horacio Keller

Independent Researcher, Kékkut, Hungary.

The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes, shortly recapitulates the prime-number-formula and the complete-prime-number-formula, the proof of the set of primes as continuum. The theoretical evaluation is followed in annexes by numerical evaluation of the theoretical results and of different constants, which represent inherent properties of the set of primes.

Density of Primes, Prime-Number-Formula, Complete-Prime-Number-Formula, Goldbach’s Conjecture, Twin Primes, K-Tuples of Primes, Primes as Continuum

Doroszlai, P. and Keller, H. (2023) The Integral of the Inverse of the Primes. Advances in Pure Mathematics, 13, 250-266. doi: 10.4236/apm.2023.135018.