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 \( 10000P \)

×

Problem Loading...

Note Loading...

Set Loading...