Prime Number Checker

A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself. The first primes are 2, 3, 5, 7, 11, and 13. Note that 2 is the only even prime, since every other even number is divisible by 2. Numbers greater than 1 that are not prime are called composite numbers.

No. By the modern definition, a prime must have exactly two distinct divisors, and 1 has only one (itself). Excluding 1 also preserves the fundamental theorem of arithmetic, which says every integer greater than 1 has exactly one prime factorization. If 1 were prime, you could add factors of 1 endlessly and factorizations would no longer be unique.

It uses optimized trial division. After ruling out divisibility by 2 and 3, it only tests candidate divisors of the form 6k ± 1 up to the square root of the number. This works because any composite number must have at least one factor no larger than its square root, so if no divisor is found by then, the number is prime.

Prime factorization expresses a number as a product of prime numbers, for example 60 = 2 × 2 × 3 × 5. Every integer greater than 1 has exactly one such factorization, a result known as the fundamental theorem of arithmetic. It is used to simplify fractions, find greatest common divisors and least common multiples, and underpins much of number theory.

Primes are the building blocks of the integers: every whole number greater than 1 is either prime or a unique product of primes. They are also central to modern cryptography: systems like RSA rely on the fact that multiplying two large primes is easy, but factoring the result back into those primes is computationally very hard.