# Prime - number theory [duplicate]

Why is the digit 1 is not a prime number? 1 can be devided by 1 and itself.

I think it's because we can express like 1= 1x1x1 ... is it true or not?

• Simple because, by definition of prime numbers, it must be larger of $1$ or smaller than $-1$. – user164524 Apr 15 '15 at 20:41
• Also, notice that if $1$ is a prime number, then the fundamental theorem of arithmetic won't give a unique prime factorization, since $1^n = 1$ for any $n\in\mathbb{Z}$. – noobProgrammer Apr 15 '15 at 20:42
• It is not prime to justify multiple theorems and results in number theory. The fundamental theorem of arithmetic especially. @noobProgrammer beat me to it. – Addison Apr 15 '15 at 20:43
• Prime numbers have four divisors, 1 has only two. – mvw Apr 15 '15 at 20:44
• @mvw Apparently, you allow also negative divisors. – Peter Aug 15 '18 at 13:58