3 papers
math.NT2026
Faster enumeration of primes
David Harvey
We describe several new algorithms for finding all prime numbers up to a given bound , achieving the first ever speedup by a positive power of over the ancient sieve of…
math.NT2026
Deterministic methods for finding elements of large multiplicative order
David Harvey, Markus Hittmeir
We revisit the problem of rigorously and deterministically finding elements of large order in the multiplicative group of integers modulo a natural number . Solving this problem…
cs.CC2025
Integer multiplication is at least as hard as matrix transposition
David Harvey, Joris van der Hoeven
Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an binary mat…