arXiv subjects

Lachlan Dunn

Publications and source records attributed to Lachlan Dunn.

2 recordsLinked to original sources

arXiv2026

An Explicit Result for the Sum of Two Almost Primes

We show that every $N \geq 2$ can be written as the sum of positive integers $a$ and $b$ where $\Omega(ab) \leq 40$. The result is obtained through the direct application of an explicit lower bound Selberg sieve along with some computation and optimisation.

math.NT↗

arXiv2025

Improved Upper Bound on Brun's Constant Under GRH

Brun's constant is the summation of the reciprocals of all twin primes, given by $B=\sum_{p \in P_2}{\left( \frac{1}{p} + \frac{1}{p+2}\right)}$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B < 2.1594$.

math.NT↗