Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions

We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. report—contrary conventional assumptions—that differentiation of discontinuous functions (DDF) exists in the set Q, which becomes central algorithms for quantum computation. DDF have been thought exist classical sense, using distributions. However, distributions still is defined terms mathematical real-numbers (MRN), and do address Problem Closure, here investigated. These facts lead contradictions MRN, solved work, providing new unbounded class solutions mechanics (QM), that were always there (just hidden), allowing without distributions, or MRN. It worthwhile see only mathematics, avoid prejudices found physics, as reforms both general relativity QM. This confirms opinions Nicolas Gisin MRN are non-computable with probability 1, Niels Bohr physics reality, it fitting story about reality. Mathematics can get closer surprisingly. just base mathematics on nature, how defines nature.