Prime Successor Irreducibility: Turing Machine Complexity, Kolmogorov Complexity, and Weakness-Based Formulations

ArXi:2605.12504v1 Announce Type: cross We develop conjectures and theorems expressing the idea that the prime sequence exhibits computational irreducibility in the transition from one prime to its successor. Informally, given a prime pp p, no general algorithm can compute the least prime greater than pp p substantially faster than sequentially testing candidates for primality, except possibly on sparse input sets. Our framework proceeds along complementary lines.