Why is the number 1 neither prime nor composite?

Answer 1

1 and 0 are special cases in many situations. 1 is not prime simply by definition. The reason is, in part, because it does not help us factor larger integers. We often ask what are the prime factors of N? If 1 were prime, there would be an infinite number of prime factors.

1 is not considered composite, again by definition: composite numbers are the product of two or more integers greater than 1.

Answer 2

If it were composite, it would have factors other than 1 and itself (and their negatives). So it isn't composite. That part is easy.

The reasons 1 isn't regarded as prime are a bit more subtle. The biggest reason is that the Fundamental Theorem of Arithmetic -- namely, that integers can be factored into primes in a unique way -- would no longer be true.

But the definitional choice could have legitimately gone the other way. Instead of awkwardly talking some of the time about "primes and/or 1", we could instead be awkwardly talking at other times about "primes other than 1".

Answer 3

well I've heard it's considered as a prime number