added overview readme

loops/README.md

@@ -0,0 +1 @@
+# Loops

loops/primes/bak

@@ -0,0 +1,12 @@
+def is_prime(n: int) -> bool:
+    # TODO: implement
+    return False
+
+
+def next_prime(n: int) -> int:
+    return -1
+
+
+def prime_factorize(n: int) -> list[int]:
+    # TODO: implement
+    return []

loops/primes/primes.py

@@ -1,12 +1,36 @@
 def is_prime(n: int) -> bool:
-    # TODO: implement
-    return False
+    if n < 2:
+        return False
+
+    for i in range(2, n // 2 + 1):
+        if n % i == 0:
+            return False
+
+    return True
 
 
 def next_prime(n: int) -> int:
-    return -1
+    return n + 1 if is_prime(n + 1) else next_prime(n + 1)
 
 
+def next_prime_iterative(n: int) -> int:
+    num = n + 1
+    while not is_prime(num):
+        num += 1
+    return num
+
 def prime_factorize(n: int) -> list[int]:
-    # TODO: implement
-    return []
+    prime_factors: list[int] = []
+    num = n
+    prime = 2
+    while num > 1:
+        if num % prime == 0:
+            prime_factors.append(prime)
+            num //= prime
+            prime = 2
+        else:
+            prime = next_prime(prime)
+    return prime_factors
+
+if __name__ == "__main__":
+    prime_factorize(10)