Does Zeta Pick Brilliantly?

Define a brilliant number to be a number $x$ such that $x^{2014} \pmod {100}$ and $x^{4102} \pmod{100}$ are both prime. If Zeta picks 2 numbers from $1$ through $100$ , inclusive, let the probability that both of these numbers are brilliant be $P$ . Compute the greatest integer less than $10000P$