Add project euler problem 50

Author: Hyftar

project_euler/problem_50/__init__.py

@@ -0,0 +1,76 @@
+"""
+https://projecteuler.net/problem=50
+Consecutive prime sum
+
+Problem 50
+
+The prime 41, can be written as the sum of six consecutive primes:
+41 = 2 + 3 + 5 + 7 + 11 + 13
+
+This is the longest sum of consecutive primes that adds to a prime below
+one-hundred.
+
+The longest sum of consecutive primes below one-thousand that adds to a prime,
+contains 21 terms, and is equal to 953.
+
+Which prime, below one-million, can be written as the sum of the most
+consecutive primes?
+"""
+
+
+def sieve(n: int) -> list:
+    """
+    Sieve of Erotosthenes
+    Function to return all the prime numbers up to a certain number
+    https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+    >>> sieve(3)
+    [2]
+
+    >>> sieve(50)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+    """
+    is_prime = [True] * n
+    is_prime[0] = False
+    is_prime[1] = False
+    is_prime[2] = True
+
+    for i in range(3, int(n**0.5 + 1), 2):
+        index = i * 2
+        while index < n:
+            is_prime[index] = False
+            index = index + i
+
+    primes = [2]
+
+    for i in range(3, n, 2):
+        if is_prime[i]:
+            primes.append(i)
+
+    return primes
+
+
+def solution() -> int:
+    """
+    Returns the solution of the problem
+    >>> solution()
+    997651
+    """
+    primes = sieve(1_000_000)
+    length = 0
+    largest = 0
+
+    for i in range(len(primes)):
+        for j in range(i + length, len(primes)):
+            sol = sum(primes[i:j])
+            if sol >= 1_000_000:
+                break
+
+            if sol in primes:
+                length = j - i
+                largest = sol
+
+    return largest
+
+
+if __name__ == "__main__":
+    print(solution())