Primality test and primes enumeration using odd numbers indexation
Marc Wolf, Fran\c{c}ois Wolf

TL;DR
This paper introduces a novel indexing method for odd numbers to improve primality testing and prime enumeration, enhancing computational efficiency in classical algorithms like Atkin and Pritchard sieves.
Contribution
The paper presents a new odd number indexing scheme and adapts existing primality algorithms to leverage this for faster computation.
Findings
Reduced input size leads to constant-time improvements
Applied indexing to Atkin sieve with similar efficiency gains
Extended technique to Pritchard wheel sieve with comparable results
Abstract
Odd numbers can be indexed by the map k(n)=(n-3)/2, n belonging to 2N+3. We first propose a basic primality test using this index function that was first introduced in article (8). Input size of operations is reduced which improves computational time by a constant. We then apply similar techniques to Atkin prime-numbers sieve which uses modulus operations and finally to Pritchard wheel sieve, in both case yielding similar results.
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