Created problem_41 in project_euler

project_euler/problem_41/__init__.py

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+#

project_euler/problem_41/sol1.py

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+from math import sqrt
+from typing import List
+from itertools import permutations
+
+"""
+We shall say that an n-digit number is pandigital if it makes use of all the digits
+1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
+What is the largest n-digit pandigital prime that exists?
+"""
+
+"""
+All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
+So we will check only 7 digit panddigital numbers to obtain the largest possible
+pandigital prime.
+"""
+
+
+def is_prime(n: int) -> bool:
+    """
+    Returns True if n is prime,
+    False otherwise.
+    >>> is_prime(67483)
+    False
+    >>> is_prime(563)
+    True
+    >>> is_prime(87)
+    False
+    """
+    if n % 2 == 0:
+        return False
+    for i in range(3, int(sqrt(n) + 1), 2):
+        if n % i == 0:
+            return False
+    return True
+
+
+def compute_pandigital_primes(n: int) -> List[int]:
+    """
+    Returns a list of all n-digit pandigital primes.
+    >>> compute_pandigital_primes(2)
+    []
+    >>> max(compute_pandigital_primes(4))
+    4231
+    >>> max(compute_pandigital_primes(7))
+    7652413
+    """
+    pandigital_str = "".join(str(i) for i in range(1, n + 1))
+    perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
+    return [num for num in perm_list if is_prime(num)]
+
+
+if __name__ == "__main__":
+    print(f"{max(compute_pandigital_primes(7)) = }")