The number 1 is neither composite nor prime.
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There are more composite numbers. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.
1 and 0 are neither composite or prime numbers
There is no name for numbers which are neither prime nor composite.
Prime numbers have two factors. Composite have more than two. Neither (one and zero) have less than two.
Zero and one are neither composite nor prime.