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

Mario Ziller; John F. Morack

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arXiv · 1706.00317

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

Mario Ziller·John F. Morack

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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.

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Mario Ziller, John F. Morack. 2017-06-01. Divisibility in paired progressions, Goldbach's conjecture, and the infinitude of prime pairs. https://arxiv.org/abs/1706.00317

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