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

  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},
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
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A systematic analysis of primality testing under adversarial conditions, where the numbers being tested for primality are not generated randomly, but instead provided by a possibly malicious party, and promotes the Baillie-PSW primality test which is both efficient and conjectured to be robust even in the adversarial setting for numbers up to a few thousand bits.
The least quadratic non residue
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It is proved that the joint distribution of the quadratic characters of the yi 's deviates from the distribution of independent fair coins by no more than t(3 + xfi-)/P, and the randomness complexity of finding these patterns in polynomial time is explored.
Conditional bounds for the least quadratic non-residue and related problems
The existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression are improved and the classical conditional bounds of Littlewood for L-functions at s=1 are refined.
Prime Numbers: A Computational Perspective
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New distributed algorithms for fast sign detection in residue number systems (RNS)
Lower Bounds for Least Quadratic Non-Residues
Let p be a prime, and let n p denote the least positive integer n such that n is a quadratic non-residue mod p. In 1949, Fridlender [F] and Salie [Sa] independently showed that \( {n_p} = \Omega