# Definition of a prime number

On the front page is a response by an SD staff member to the question of whether 0 is even or odd. They go on to comment on the status of 1. Now, the definition they give is “having no divisors except itself and 1.”
They use this to show that one is neither prime nor not prime.
But I learned in school that a prime number is a positive number that has exactly two factors, 1 and itself.
This would seem to exclude 1.
Further more, the claim that all non-prime numbers are composites seems questionable. What about irrationals? Imaginary? Infinite?
http://www.straightdope.com/mailbag/mzeroeven.html

Prime/composite only makes sense in the set of natural numbers. The set is understood to be positive integers, that’s why you don’t need to address the superset of rational numbers, or the larger set of reals.

1 is neither composite nor prime; it is a unit.

I don’t understand why he spent time in his answer arguing that zero is not even in the set of natural numbers, because zero is not
a natural number. If you’re answering the question of whether a given number is even, why talk about sets the number isn’t in?

Also, in the conjecture bit, he uses the word ‘uniquely’: every even number higher than two can be uniquely expressed by the sum of two primes,

But 10 = 7+3 = 5+5.
16 = 11+5 = 13+3

As you’ve shown, that was just a mistake. The “uniquely” is NOT part of the conjecture, and never has been. The writer probably got carried away with uniqueness based on prime factorizations.

Obviously, the writer was not Cecil.

Yep. This is being discussed in the mailbag forum.

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Sorry about the “uniqueness”, it’s what comes of drafting too quickly and not proofing well. Too much spiked holiday egg nog.

The reason we went to such lengths to find an explanation of how zero could be considered NOT an even number, is that was what the poser of the question was asking. She had some memory of some situation where zero was not considered even, and we were trying to figure out what that situation would be. If the question had just been, “Is zero odd or even,” we wouldn’t have given it a moment’s thought. But the question was essentially, “I remember some circumstance in which zero is considered neither odd nor even.”

Having said that, we are now closing this topic here, and moving it to the forum called CECIL’S MAILBAG.