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A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The smallest twenty-five prime numbers (all the prime numbers under 100) are:
: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 .
An infinitude of prime numbers exists, as demonstrated by Euclid around 300 BC, although the density of prime numbers within natural numbers is 0. The number 1 is by definition not prime. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any positive intege...