{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T23:02:31Z","timestamp":1778540551729,"version":"3.51.4"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"245","license":[{"start":{"date-parts":[[2004,6,11]],"date-time":"2004-06-11T00:00:00Z","timestamp":1086912000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Schmutz Schaller\u2019s conjecture regarding the lengths of the hexagonal versus the lengths of the square lattice is shown to be true. The proof makes use of results from (computational) prime number theory. Using an identity due to Selberg, it is shown that, in principle, the conjecture can be resolved without using computational prime number theory. 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