Add project euler problem 50 (#3016)

* Add project euler problem 50

* Apply format changes

* Descriptive function/parameter name and type hints

Co-authored-by: Dhruv Manilawala <[email protected]>

Author: Hyftar

project_euler/problem_050/__init__.py

@@ -0,0 +1,85 @@
+"""
+Project Euler Problem 50: https://projecteuler.net/problem=50
+
+Consecutive prime sum
+
+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?
+"""
+from typing import List
+
+
+def prime_sieve(limit: int) -> List[int]:
+    """
+    Sieve of Erotosthenes
+    Function to return all the prime numbers up to a number 'limit'
+    https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+
+    >>> prime_sieve(3)
+    [2]
+
+    >>> prime_sieve(50)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+    """
+    is_prime = [True] * limit
+    is_prime[0] = False
+    is_prime[1] = False
+    is_prime[2] = True
+
+    for i in range(3, int(limit ** 0.5 + 1), 2):
+        index = i * 2
+        while index < limit:
+            is_prime[index] = False
+            index = index + i
+
+    primes = [2]
+
+    for i in range(3, limit, 2):
+        if is_prime[i]:
+            primes.append(i)
+
+    return primes
+
+
+def solution(ceiling: int = 1_000_000) -> int:
+    """
+    Returns the biggest prime, below the celing, that can be written as the sum
+    of consecutive the most consecutive primes.
+
+    >>> solution(500)
+    499
+
+    >>> solution(1_000)
+    953
+
+    >>> solution(10_000)
+    9521
+    """
+    primes = prime_sieve(ceiling)
+    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 >= ceiling:
+                break
+
+            if sol in primes:
+                length = j - i
+                largest = sol
+
+    return largest
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")