Comments by "kazedcat" (@kazedcat) on "Is 1 a Prime Number?" video.

  1. Not necessary. All negative numbers are additive inverse of naturals so -5 is an additive inverse of 5 which is a prime. So the prime decomposition of -20 is the prime decomposition of its additive inverse that is 20=2*2*5.
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  2. 1 is a special number that is neither prime nor composite. It is similar to zero who is neither positive nor negative.
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  3.  @ingiford175  The problem with defining -1 as prime is that it would turn all negative numbers composite. And it would break the fundamental theorem of arithmetic because you can extend any prime decomposition by multiplying it with (-1)²ⁿ for any natural number n. This means prime decomposition is no longer unique.
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