There's no need for a proof. The number 1 is not prime by definition.
See the very first sentence at: https://en.wikipedia.org/wiki/Prime_number
The reason we define 1 to not be prime is so that the Fundamental Theorem of Arithmetic can be stated in its simplest form. See: https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic
Also note that 1 is not composite either. It's in a special class by itself. It's often called a "unit".
1 has only one factor, it is therefore neither prime nor composite.
If one refers to the number of factors, then 1 is neither prime nor composite.....
"A prime number is a natural number which has only 2 factors, (1 and itself)"
A composite number is a natural number which has more than 2 factors"
As 1 has only one factor, (1), it does not meet the requirements of either prime or composite numbers.
However, it is interesting to note that a SQUARE number has an ODD number of factors. As 1 has one factor, it is a square number.
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