The General Solution to the Twin Prime Problem, or Constructivism vs. Analytical Atavism

Abstract

This paper proposes a fundamentally new approach to investigating the structure of the set of natural numbers based on the concept of alternative and connected numerical sets, one of which is the set of prime numbers. The method of dynamic sieves is described. By utilizing the proposed kinematic model and the theory of connected sets, a theorem is proven on the infinity of sets of n-tuple primes of arbitrary length and configuration. While the theory of connected sets expands the theorem, the theory of alternative sets deepens it, rendering the theorem global.