arXiv subjects
Publications and source records attributed to Lachlan Dunn.
We show that every $N \geq 2$ can be written as the sum of positive integers $a$ and $b$ where $Ω(ab) \leq 40$. The result is obtained through the direct application of an explicit lower bound Selberg sieve along with some computation and optimisation.
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 $B < 2.1594$.