Divisibility in paired progressions, Goldbach's conjecture, and the infinitude of prime pairs

Abstract

We investigate progressions in the set of pairs of integers ${\mathbb{Z}}^2$ and define a generalisation of the Jacobsthal function. For this function, we conjecture a specific upper bound and prove that this bound would be a sufficient condition for the truth of the Goldbach conjecture, the infinitude of prime twins, and more general of prime pairs with a fixed even difference.

10 pages, 1 figure

References in corpus (1)

• On the difference of primes

Cited by in corpus (1)

• A short note on the computation of the generalised Jacobsthal function for paired progressions