Simon N. Thomas

collaborators

2 papers

math.NT2026

Primes and almost primes between cubes

Daniel R. Johnston, Jonathan P. Sorenson, Simon N. Thomas +1

In this paper we study the problem of detecting prime numbers between all consecutive cubes. Firstly, we use a large computation to show that there is always a prime between $n^{3}$ …

math.NT2025

The sum of a prime power and an almost prime

Daniel R. Johnston, Simon N. Thomas

For any fixed $k \geq 2$ , we prove that every sufficiently large integer can be expressed as the sum of a $k$ th power of a prime and a number with at most $M (k) = 6 k$ prime factors. F…