Prime or Composite

Some numbers have only two factors, 1 and themselves. 13 is one: nothing from 2 to 12 divides it. Such a number is prime. A number with more than two factors, like 15 (1, 3, 5 and 15), is composite: it can be built by multiplying smaller numbers, 3 × 5.

The number 1 is neither. It has just one factor, itself, so it falls short of the two a prime needs. This is not a fussy exception: the next chapter breaks numbers into primes, and that only works if 1 is left out, because 1 could be multiplied in any number of times without changing anything.

2 is the only even prime. Every other even number has 2 as a factor as well as 1 and itself, so it has at least three factors. The primes below 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.