Miller: conditional efficient deterministic primality testing

What changed

Scientific scope

Miller gives deterministic compositeness-witness algorithms and establishes polynomial-bit-length primality testing conditional on the stated Extended Riemann Hypothesis, alongside number-theoretic functional reductions under declared assumptions. Exact 1976 J. Comput. Deterministic polynomial bit-length primality result assumes source Appendix ERH for stated Dirichlet-character L-functions; unconditional test has a different non-polynomial-bit-length bound. Perfect-power/root/divisor checks and small witnesses remain. Source abstract shorthand and refined theorem bit costs differ; damaged exponent/log glyphs not certified, no guessed exact complexity pasted in. Eulerphi/Carmichael/factorization equivalences and period oracle reductions retain ERH and source reduction/size conditions; recognizable factorization graph is not efficient general factor generation. No resolution of ERH, Pvs NP or factoring. Tiny own modular checks illustrate witnesses, not inherited analytic lemmas/globalproof. No independent scientific certification.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Gary L. Miller · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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