Vijay picks two random distinct primes 1 \leq p, q \leq 10^{4}. Let r be the probability that 3^{2205403200} \equiv 1 \bmod p q. Estimate r in the form 0 . a b c d e f, where a, b, c, d, e, f are decimal digits.
Vijay picks two random distinct primes 1 \leq p, q \leq 10^{4}. Let r be the probability that 3^{2205403200} \equiv 1 \bmod p q. Estimate r in the form 0 . a b c d e f, where a, b, c, d, e, f are decimal digits.