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MillerโRabin is a fast primality test that uses modular exponentiation to detect compositeness with very high reliability.
Eulerโs Theorem says that if a and n are coprime, then a raised to the power ฯ(n) is congruent to 1 modulo n.
Fast exponentiation (binary exponentiation) computes a^n using repeated squaring in O(log n) multiplications.
Prime factorization expresses any integer greater than 1 as a product of primes raised to powers, uniquely up to ordering.