## 12 Citations

Two Algorithms to Find Primes in Patterns

- Computer Science, MathematicsMath. Comput.
- 2020

Two algorithms are presented that find all integers $x$ where $\max{ f_i(x) \le n$ and all the $f_i (x)$ are prime and prove correctness unconditionally, but the running time relies on two unproven but reasonable conjectures.

A logarithmic improvement in the Bombieri–Vinogradov theorem

- MathematicsJournal de Théorie des Nombres de Bordeaux
- 2019

In this paper we improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowing a smooth…

Computational Complexity Theory and the Philosophy of Mathematics†

- Computer SciencePhilosophia Mathematica
- 2019

This paper highlights the significance of complexity theory relative to questions traditionally asked by philosophers of mathematics while also attempting to isolate some new ones — e.g., about the notion of feasibility in mathematics, the $\mathbf{P} \neq \ mathbf{NP}$ problem and why it has proven hard to resolve, and the role of non-classical modes of computation and proof.

On Toric Orbits in the Affine Sieve

- MathematicsExperimental Mathematics
- 2019

Abstract We give a detailed analysis of a probabilistic heuristic model for the failure of “saturation” in instances of the Affine Sieve having toral Zariski closure. Based on this model, we…

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

- Computer Science, MathematicsArXiv
- 2019

This set of three companion manuscripts/articles unveils new results on primality testing and reveal new primalityTesting algorithms enabled by those results and reveals close connections between the state-of-the-art Miller-Rabin method and the renowned Euler-Criterion.

Primality Testing is Polynomial-time: A Mechanised Verification of the AKS Algorithm

- Computer Science
- 2019

A formalisation of the Agrawal-Kayal-Saxena (AKS) algorithm, a deterministic polynomial-time primality test, and an implementation of the AKS algorithm that is suitable for loop analysis of complexity, as well as introducing an approach to study the time complexity of simple loops.

Strongly nonzero points and elliptic pseudoprimes

- Mathematics
- 2019

We examine the notion of strongly non-zero points and use it as a tool in the study of several types of elliptic pseudoprimes. Moreover, we give give some probabilistic results about the existence of…

N ov 2 01 7 A quantum primality test with order finding

- 2018

Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat’s theorem. For an…

A quantum primality test with order finding

- Physics, Mathematics
- 2017

Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an…

On Deterministic Reduction of Factoring Integers to Computing the Exponents of Elements in Modular Group

- Mathematics, Computer ScienceFundam. Informaticae
- 2017

In the paper we prove that all but at most x/A(x) positive integers n ≤ x can be completely factored in deterministic polynomial time C(x), querying the prime decomposition exponent oracle at most…