Input interpretation:

prime number | basic definitions


A positive integer that has exactly one positive integer divisor other than 1 (i.e., no factors other than 1 and itself).  Prime numbers are often simply called primes.

Detailed definition:

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1, meaning it is a number that cannot be factored. For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization 24 = 2^3·3), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.\nWhile the term "prime number" commonly refers to prime positive integers, other types of primes are also defined, such as the Gaussian primes.

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