3 problems

Subpandigital and subpenholodigital prime digit-sum conjecture. For $b>4$, the smallest subpandigital prime or smallest subpenholodigital prime $n$ satisfies…

Pandigital and penholodigital prime digit-sum conjecture. For $b>3$, the smallest pandigital prime or penholodigital prime $n$ satisfies $s_b(n)=b(b-1)/2+2$ if $b$ is of the form…

Subpandigital and subpenholodigital square existence conjecture. Suppose $b>7$. A strict subpandigital square and a strict subpenholodigital square in base $b$ exist if and only if…