---
book: 7
number: 32
id: "VII.32"
kind: "theorem"
uses: ["[[book-7/proposition-31]]"]
source: "https://scaife.perseus.org/reader/urn:cts:greekLit:tlg1799.tlg001.perseus-eng2:7.prop.32"
license: "CC-BY-SA-4.0"
---

# VII.32

*Any number either is prime or is measured by some prime number.*

## Proof

Let *A* be a number; I say that *A* either is prime or is measured by some prime number.

If now *A* is prime, that which was enjoined will have been done.

But if it is composite, some prime number will measure it. [[book-7/proposition-31|VII. 31]]

Therefore any number either is prime or is measured by some prime number. Q. E. D.