Why 1 is not prime number?

Answer 1

It's a question of how "prime" is defined. Mathematicians have chosen not to include 1 in their set of prime numbers, possibly because they feel it makes things easier.

Every positive integer can be written as a product of prime numbers (prime factorization). In fact, every positive integer has only one prime factorization. (Reordering the primes doesn't count, e.g. 2x3x3 is the same as 3x2x3.) This would no longer be true if 1 was a Prime number. For instance: 14 = 2x7 = 1x2x7 = 1x1x2x7 = 1x1x1x2x7. Every positive integer would have infinitely many prime factorizations. You's have to rewrite the theorem to say "...only one prime factorization WITHOUT A 1", which would be more awkward.

There are probably more examples out there, but I can't think of any good ones at the moment.