Kevin Schimmel

Prime Values of p³ − 2 over Prime Inputs: Reproducible Computational Edition with the p³ + 2 Mirror Lane

This paper studies prime inputs p for which p^3 - 2 or p^3 + 2 is prime and states two corresponding infinitude conjectures. For every prime p > 3, if p mod 3 = 2, then p^3 - 2 is composite. If p mod 3 = 1, then p^3 + 2 is composite. In each case, the expression with the opposite...

Prime Values of p³ − 2 over Prime Inputs: Reproducible Computational Edition with the p³ + 2 Mirror Lane

This paper studies prime inputs p for which p^3 - 2 or p^3 + 2 is prime and states two corresponding infinitude conjectures. For every prime p > 3, if p mod 3 = 2, then p^3 - 2 is composite. If p mod 3 = 1, then p^3 + 2 is composite. In each case, the expression with the opposite...