diff --git a/math/number_theory/notes.page b/math/number_theory/notes.page
index 211e4d5..958e093 100644
--- a/math/number_theory/notes.page
+++ b/math/number_theory/notes.page
@@ -61,3 +61,17 @@ b\mid a &\to bc\mid ac\\
 and
 $$c\mid a \cdot c\mid b \to c\mid ma + nb$$
 for all integers $m$ and $n$
+
+A number $p$ is *prime* if:
+
+i. $p > 1$
+ii. $p$ has no positive divisors except $1$ and $p$
+
+The number $1$ is not considered prime.
+
+A number is *composite* if it is greater than $1$ and not prime.
+
+**Theorem 1**
+: Every positive integer, except $1$, is a product of primes.
+
+