A Prime number is a positive integer that has exactly two different factors: 1 and itself.
This is why 1 is not a prime number: it has the factors 1 and itself, but they are the same - it does not have exactly two different factors.
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Square numbers can't be prime. They have too many factors.
2 and 3 are the prime factors of 36. Of the factors of 36, 2 and 3 are the only prime numbers.
The new number has four factors: 1, the two prime numbers and the new product.
The number 1 is neither composite nor prime.
Just the number two.