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1 solution
There are a couple of reasons it makes sense not to include 1 in the set of primes:
Multiples of prime numbers are not prime, if we defined 1 as prime we would have to make an exception to this rule
Integers greater than 1 can be expressed as the product of a single set (ignoring order) of primes, for example 10 has prime factors 2 and 5, if 1 were prime we could also express 10 as the product of 1, 2 and 5 or even 1, 1, 1, 2 and 5.
By treating 1 as a special number, but not a prime, we avoid complicating these rules with exceptions for 1.