哥德巴赫猜想
Victor Ufnarovski and Bo Åhlander have detailed the function's connection to famous number-theoretic conjectures like the twin prime conjecture, the prime triples conjecture, and Goldbach's conjecture. For example, Goldbach's conjecture would imply, for each the existence of an so that . The twin prime conjecture would imply that there are infinitely many for which .