A conjecture of Schmutz Schaller [17, p. 201] regarding the lengths of the hexagonal versus the lengths of the square lattice is shown to be true. The proof uses results from (computational) prime number theory and from [10]. Using an identity due to Selberg, it is shown that the conjecture can in principle be also resolved without using computational prime number theory. By our approach, however, this would require a huge amount of computation.

Numerical Algorithms and Problems (acm F.2.1)
Primes in progressions (msc 11N13), Analytic computations (msc 11Y35), Evaluation of constants (msc 11Y60)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Moree, P, & te Riele, H.J.J. (2002). The hexagonal versus the square lattice. Modelling, Analysis and Simulation [MAS]. CWI.