eli5-Why is the number 1 not considered a prime number even though there isn’t any number that divides it?
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Every whole number grater than 1 can be written as the product of prime numbers in a UNIQUE way. If you add 1 to the mixture every number has an infinite amout of correct prime factorisations. Like 12 is 2×2×3 and this is its only unique prime factorisation. If 1 is a prime 12 = 2×2×3 = 2×2×3×1 = 2×2×3×1×1 = 2×2×3×1×1×1×…×1.
Having only one prime factorisation for a composite number simplifies a lot of things and without it some proofs wouldn’t work.
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