hacktoberfest

Author: willtryagain

project_euler/problem_050/sol1.py

@@ -1 +1,79 @@
-
+"""
+Project Euler Problem [50]: https://projecteuler.net/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 is_prime(number: int) -> [bool]:
+    """
+    Test to see if the number is prime
+    """
+    i = 2 # begin from the smallest prime
+
+    # if the number is a composite then it will atleat have a
+    # factor less than equal to its square root
+    
+    while i * i <= number:
+        # if number is divisible by i then i is a factor of number
+        if  number % i == 0:
+            return False
+        i += 1
+    return True
+
+def sieve_of_eratosthenes(limit: int) -> [list]:
+    """
+    Returns a list of boolean values that indicate
+    whether number at a given index is prime
+    """
+    is_prime_number = [True] * (limit + 1)
+    i = 2 # begin from the smallest prime
+    while i * i <= limit:
+        if is_prime_number[i]:
+            for j in range(2*i, limit + 1, i):
+                is_prime_number[j] = False
+        i += 1
+    return is_prime_number
+
+def solution(limit: int = 1_000_000):
+    """
+    Get the prime number less than limit which is
+    longest sum of consecutive primes.
+
+    >>> solution(100)
+        41
+    >> solution(1000)
+        953
+    """
+    prime_number = 0 #result
+    max_length = 0 #length 
+    is_prime_number = sieve_of_eratosthenes(limit)
+    primes = []
+    for i in range(2, limit):
+        if is_prime_number[i]:
+            primes.append(i)
+    for i in range(len(primes)):
+        total = 0
+        for j in range(i, len(primes)):
+            total += primes[j]
+            if total >= limit:
+                break
+            if is_prime(total):
+                if max_length < j - i + 1:
+                    prime_number = total
+                    max_length = j - i + 1
+        
+    return prime_number
+
+if __name__ == "__main__":
+    print(f"{solution() = }")
+
+