Deterministic Primality Proving on Proth Numbers
Tsz-Wo Sze
TL;DR
This paper introduces a deterministic algorithm for testing the primality of Proth numbers, providing explicit time complexity bounds without relying on unproven hypotheses.
Contribution
The paper presents a new deterministic primality testing algorithm specifically for Proth numbers with proven time complexity bounds, advancing number theory methods.
Findings
Algorithm runs in expected O((t log t + log N) log N) time
Worst-case complexity is O((t log t + log N) log^2 N)
No unproven hypotheses assumed
Abstract
We present an algorithm to decide the primality of Proth numbers, N=2^e t+1, without assuming any unproven hypothesis. The expected running time and the worst case running time of the algorithm are O ((t log t + log N)log N) and O ((t log t + log N) log^2 N) bit operations, respectively.
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Taxonomy
TopicsAlgorithms and Data Compression · Numerical Methods and Algorithms · semigroups and automata theory