# Does Zeta Pick Brilliantly?

Number Theory Level pending

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 $$10000P$$

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