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A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. Primes are the fundamental building blocks of all integers — every integer > 1 is either prime or can be uniquely factored into primes (Fundamental Theorem of Arithmetic).

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1. 1Trial division: test if n is divisible by any integer from 2 to √n
2. 2If no divisor found, n is prime
3. 3Sieve of Eratosthenes: efficiently finds all primes up to a limit
4. 4For large numbers, probabilistic tests like Miller-Rabin are used

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