Faster integer multiplication using plain vanilla FFT primes

TL;DR

This paper proposes a faster integer multiplication algorithm based on plain vanilla FFT primes, achieving near-linearithmic complexity under a conjectural assumption about primes in arithmetic progressions.

Contribution

It introduces a novel approach leveraging conjectural bounds on primes to improve integer multiplication complexity using FFT primes.

Findings

Achieves O(n log n 4^{log^* n}) complexity under conjecture.

Relies on an assumed upper bound for the least prime in an arithmetic progression.

Provides theoretical analysis of the algorithm's efficiency.

Abstract

Assuming a conjectural upper bound for the least prime in an arithmetic progression, we show that n-bit integers may be multiplied in O(n log n 4^(log^* n)) bit operations.