PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts

@article{Phatak2019PPTNL,
  title={PPT: New Low Complexity Deterministic Primality Tests Leveraging Explicit and Implicit Non-Residues. A Set of Three Companion Manuscripts},
  author={Dhananjay S. Phatak and Alan T. Sherman and Steven D. Houston and Andrew Henry},
  journal={ArXiv},
  year={2019},
  volume={abs/1908.06964}
}
In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as lemmas/corollaries/claims whenever we have complete analytic proof(s); otherwise the results are introduced as conjectures. In Part/Article 1, we start with the Baseline Primality Conjecture~(PBPC) which enables deterministic primality detection with a low complexity = O… 
Bounds on the Range(s) of Prime Divisors of a Class of Baillie-PSW Pseudo-Primes
TLDR
It is shown that if a Williams' number is encountered during a search in accordance with all of the conditions in that recipe~\cite{pomerance1984there}~; then it must also be a Baillie-PSW pseudoprime, and new analytic bounds are derived on the prime-divisors of aWilliams' Number.

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