Is the number 1 prime or composite?

The number one is neither prime nor composite. Prime numbers are positive integers greater than one that are evenly divisible only by themselves and one. Composite numbers are positive integers that have divisors other than themselves and one.

One cannot be prime because it does not meet the criteria of being greater than one. Until the 1800s, the number one was considered prime, but the body of mathematical thinking changed to come in line with the fundamental theorem of arithmetic, which dictates that every number has a unique prime factorization. If one were considered prime, it would have to be included in the prime factorization of all numbers.