The construction turns tests for primality into a formula that isolates the first prime beyond a prescribed integer. The point is the exact arithmetic mechanism, rather than a practical prime-search algorithm.
Background
Elementary number theory, factorials, and divisibility.
Read the full exposition
The complete argument is available as a PDF.
Revision history ·
Revised October 7, 2026: clarified the introduction while preserving the problem’s IRC provenance. The theorem, proof, and appendix are unchanged.