= Infinitely many primes congruent to one modulo six
{title2=$\#\{p\text{ prime}:p\equiv1\pmod6\}=\infty$}
Assume that $x^2\equiv-3\pmod p$ with $p>3$ implies $p\equiv1\pmod6$. For a finite list of primes in that residue class, let $P$ be their product. Every prime divisor of $4P^2+3$ is greater than three and satisfies that quadratic <modular congruence>, hence has residue one modulo six. None is listed because $4P^2+3\equiv3$ modulo a listed prime.
// Target: combinatorics.bigb
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