On the complexity of computing prime tables on a Turing machine

TL;DR

This paper establishes that computing the prime table up to n on a multitape Turing machine can be done within an O(n log n) complexity, providing a precise measure of the computational effort involved.

Contribution

It proves an upper bound of O(n log n) for prime table computation on a multitape Turing machine, clarifying the complexity of this fundamental problem.

Findings

Prime table computation is O(n log n) on a multitape Turing machine.

Provides a formal complexity bound for prime number generation.

Clarifies the computational limits of prime table algorithms.

Abstract

We prove that the complexity of computing the table of primes between $1$ and $n$ on a multitape Turing machine is $O(n \log n)$.