Prime numbers

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A prime number is a natural number that has exactly two positive divisors, namely 1 and the number itself. So 2 is a prime because its only divisors are 1 and 2; 3 and 5 are primes for the same reason, that their only divisors are 1 and themselves. But 4 is not a prime because 1, 2, and 4 are all divisors of 4, so 4 has three divisors and is therefore not a prime. The first nine primes are 2, 3, 5, 7, 11, 13, 17, 19, and 23. There are infinitely many primes, that is, there is no ‘last’ prime number. Note that zero is not a prime number since every natural number divides zero, and one is not a prime number since it has only one divisor, namely itself.
The simplest means of sifting out the positive primes numbers from the natural numbers is to use the sieve of Eratosthenes.
Integers that are not 0, ±1, or prime, are called composite.