Daniel R. Johnston

collaborators

3 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…

math.NT2025

Almost primes between all squares

Adrian W. Dudek, Daniel R. Johnston

We prove that for all $n \geq 1$ there exists a number between $n^{2}$ and $(n + 1)^{2}$ with at most 4 prime factors. This is the first result of this kind that holds for every $n \geq 1$ …