From d403da53db27a824fc44a328d602c52b37f0d125 Mon Sep 17 00:00:00 2001
From: Emile Clark-Boman <eclarkboman@gmail.com>
Date: Tue, 1 Jul 2025 18:04:00 +1000
Subject: [PATCH] Add basic tests of semi-primality and k-almost primality

---
 imp/math/numbers/functions.py |  5 +++++
 imp/math/numbers/kinds.py     |  1 +
 imp/math/primes.py            | 18 ++++++++++++++++++
 3 files changed, 24 insertions(+)
 create mode 100644 imp/math/numbers/functions.py
 create mode 100644 imp/math/numbers/kinds.py

diff --git a/imp/math/numbers/functions.py b/imp/math/numbers/functions.py
new file mode 100644
index 0000000..6cafa7f
--- /dev/null
+++ b/imp/math/numbers/functions.py
@@ -0,0 +1,5 @@
+def factorial(n: int) -> int:
+    if n == 0: return 1
+    return n * factorial(n-1)
+
+def
diff --git a/imp/math/numbers/kinds.py b/imp/math/numbers/kinds.py
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/imp/math/numbers/kinds.py
@@ -0,0 +1 @@
+
diff --git a/imp/math/primes.py b/imp/math/primes.py
index 513f61e..eaeebcb 100644
--- a/imp/math/primes.py
+++ b/imp/math/primes.py
@@ -1,5 +1,23 @@
 from math import gcd
+from imp.math.numbers import bigomega
 
+def coprime(n: int, m: int) -> bool:
+    return gcd(n, m) == 1
+
+def almostprime(n: int, k: int) -> bool:
+    '''
+    A natural n is "k-almost prime" if it has exactly
+    k prime factors (including multiplicity).
+    '''
+    return (bigomega(n) == k)
+
+def semiprime(n: int) -> bool:
+    '''
+    A semiprime number is one that is 2-almost prime.
+    Ref: https://en.wikipedia.org/wiki/Semiprime 
+    '''
+    return almostprime(n, 2)
+    
 '''
 Euler's Totient (Phi) Function
 '''