Sieve of Sundaram

maths/sieve_of_sundaram.py

@@ -0,0 +1,48 @@
+"""
+Sieve of Sundaram - Alternative prime number algorithm.
+Discovered by S. P. Sundaram in 1934.
+"""
+
+from typing import List
+
+
+def sieve_of_sundaram(limit: int) -> List[int]:
+    """
+    Find all prime numbers up to limit using Sieve of Sundaram.
+
+    >>> sieve_of_sundaram(30)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+    >>> sieve_of_sundaram(10)
+    [2, 3, 5, 7]
+    >>> sieve_of_sundaram(2)
+    []
+    """
+    if limit <= 2:
+        return []
+
+    n = (limit - 1) // 2
+    marked = [False] * (n + 1)
+
+    for i in range(1, n + 1):
+        j = i
+        while i + j + 2 * i * j <= n:
+            marked[i + j + 2 * i * j] = True
+            j += 1
+
+    primes = [2]
+    for i in range(1, n + 1):
+        if not marked[i]:
+            primes.append(2 * i + 1)
+
+    return primes
+
+
+
+if __name__ == "__main__":
+    print("Sieve of Sundaram Demo")
+    print("-" * 20)
+
+    for limit in [10, 30, 50]:
+        primes = sieve_of_sundaram(limit)
+        print(f"Primes up to {limit}: {primes}")
+        print(f"Found {len(primes)} primes")