Is 1 a prime number?

The number 1 is not a prime number. A prime number by definition is a positive integer greater than 1 that is evenly divisible by only itself and 1.

Until the 19th century, 1 was often considered a prime number. The thinking changed, however, to accommodate the fundamental theorem of arithmetic, which mandates that each number has a unique factorization. Two is the smallest prime number, because it is larger than 1 and its only factors are 1 and itself. It is also the only even prime number, because all other even numbers have 2 as a factor. The next nine prime numbers are 3, 5, 7, 11, 13, 17, 19, 23 and 29.