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A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. For example, 2, 3, 5, 7, 11, and 97 are prime numbers. The number 1 is not considered prime.

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Prime factorization is the process of breaking down a composite number into a product of prime numbers. For example, 360 = 2³ × 3² × 5. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).

This calculator supports numbers up to 10,000,000 (10 million) for generation and checking. For factorization, it can handle numbers up to 1 trillion (10¹²) efficiently.