Why 1 is not prime

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I have been told that there is some interesting mathematics to why the number 1 is not prime. Can someone explain why one is not a prime number?

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Because a prime number is a number that has exactly two distinct positive divisors.

Examples:

  • $2$ can be divided by $1$ and $2$

  • $11$ can be divided by $1$ and $11$

  • $1$ can be divided by $1$ and... $1$ so it is not prime.