dchou1618 · Jul 17, 2026 · Jul 16, 2026 · Jul 17, 2026
diff --git a/Algorithms/numerical_methods/euler/p50.py b/Algorithms/numerical_methods/euler/p50.py
@@ -0,0 +1,35 @@
+from typing import Optional
+
+
+def sieve(n: int):
+    is_prime = [True] * (n + 1)
+    if n >= 0:
+        is_prime[0] = False
+    if n >= 1:
+        is_prime[1] = False
+    primes = []
+    for p in range(2, n + 1):
+        if is_prime[p]:
+            primes.append(p)
+            for v in range(p * p, n + 1, p):
+                is_prime[v] = False
+    return is_prime, primes
+
+def consecutive_prime_sum(n: int) -> Optional[int]:
+    is_prime, primes = sieve(n)
+    longest_sum = 0
+    longest_sum_prime = None
+    pref_sums = [0]*(len(primes)+1)
+    # go through every prefix sum (pairs of start and end primes), sum should be prime
+    for i in range(1, len(pref_sums)):
+        pref_sums[i] = pref_sums[i-1] + primes[i-1]
+
+    for start in range(len(primes)):
+        for end in range(start+longest_sum+1, len(primes)+1):
+            s = pref_sums[end]-pref_sums[start]
+            if s >= n:
+                break
+            if is_prime[s]:
+                longest_sum = end-start
+                longest_sum_prime = s
+    return longest_sum_prime
diff --git a/tests/euler/p50_test.py b/tests/euler/p50_test.py
@@ -0,0 +1,13 @@
+from Algorithms.numerical_methods.euler.p50 import consecutive_prime_sum, sieve
+
+
+def test_sieve_marks_zero_and_one_as_non_prime():
+    is_prime, primes = sieve(10)
+    assert is_prime[0] is False
+    assert is_prime[1] is False
+    assert primes == [2, 3, 5, 7]
+
+
+def test_sol():
+    assert consecutive_prime_sum(n=1_000_000) == 997651
+