added tut05

Tutorium/tut05/src/primes.py

@@ -0,0 +1,34 @@
+def prime_factorization(num: int) -> tuple[int, list[int]]:
+    # our list of primefactors
+    primefactors: list[int] = []
+    # our first prime number
+    prime: int = 2
+    # we don't want to modify our number and copy it to `n`
+    n: int = num
+
+    # iterate until we find the last step the square of
+    # our prime is bigger than our rest number
+    while n != 1:
+        # if our number is dividable by our prime
+        if n % prime == 0:
+            # we can add the prime to our primefactors
+            primefactors.append(prime)
+            # and divide our rest number by the prime number
+            n //= prime
+        else:
+            # increment until next prime number
+            prime += 1
+
+    # finally return our tuple with our number and primefactors
+    return (num, primefactors)
+
+
+if __name__ == "__main__":
+    assert (sol := (100, [2, 2, 5, 5])) == (
+        res := prime_factorization(100)), f"{res} is not {sol}"
+    assert (sol := (69, [3, 23])) == (
+        res := prime_factorization(69)), f"{res} is not {sol}"
+    assert (sol := (31, [31])) == (
+        res := prime_factorization(31)), f"{res} is not {sol}"
+    assert (sol := (123490823022, [2, 3, 3, 3, 3, 7, 7, 7, 1123, 1979])) == (
+        res := prime_factorization(123490823022)), f"{res} is not {sol}"