Coprime-universality conjecture for the ternary forms in Table 1

A ternary quadratic form is coprime-universal with respect to $p$ if it represents every positive integer coprime to $p$. Coprime-universality conjecture. The ternary forms listed in Table 1 are coprime-universal for the stated primes.

These forms provide the conditional input for determining the finite test sets $S_p$ for all primes. The conjecture is left open because the relevant questions are closely related to the existence of Siegel zeros, a major open problem in number theory.