Definitions 11–14

11. A prime number is that which is measured by a unit alone.

12. Numbers relatively prime are those which are measured by a unit alone as a common measure.

13. A composite number is that which is measured by some number.

14. Numbers relatively composite are those which are measured by some number as a common measure.


Prime numbers form a very important class of numbers, and much of number theory is devoted to their analysis. The only proper divisor of a prime number is 1. The first few prime numbers are, of course, 2, 3, 5, 7, 11. Those numbers that aren’t prime are composite, for instance, 4, 6, 8, 9, 10. The number 1 holds a special position. For Euclid, it was the unit rather than a number. For modern mathematicians 1 is also a unit, but in a different sense of the word, since it has a reciprocal, namely, itself.

Numbers are relatively prime if their only common divisor is 1. For example, 6 and 35 are relatively prime (although neither is a prime number in itself). This situation is also phrased as “6 is prime to 35.” For another example, the three numbers 6, 10, and 15 are relatively prime since no number (except 1) divides all three. If the numbers aren’t relatively prime, then they’re called “relatively composite,” a rarely used term.