Primality tests for Fermat numbers and 2^(2k+1)\pm2^(k+1)+1

TL;DR

This paper introduces new elliptic curve-based primality tests for Fermat numbers and related integers, expanding the toolkit for primality verification of special forms of numbers.

Contribution

It presents novel primality tests for Fermat numbers and integers of specific forms using elliptic curves, complementing existing methods.

Findings

New primality tests for Fermat numbers and related integers

Tests are based on elliptic curve properties

Potentially more efficient verification methods

Abstract

Robert Denomme and Gordan Savin made a primality test for Fermat numbers 2^(2^k)+1 using elliptic curves. We propose another primality test using elliptic curves for Fermat numbers and also give primality tests for integers of the form 2^(2k+1)\pm2^(k+1)+1.