Created problem_35 in project_euler

project_euler/problem_35/__init__.py

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+#

project_euler/problem_35/sol1.py

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+"""
+The number 197 is called a circular prime because all rotations of the digits:
+197, 971, and 719, are themselves prime.
+There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73,
+79, and 97.
+How many circular primes are there below one million?
+
+To solve this problem in an efficient manner, we will first mark all the primes
+below 1 million using the Seive of Eratosthenes.  Then, out of all these primes,
+we will rule out the numbers which contain an even digit.  After this we will
+generate each circular combination of the number and check if all are prime.
+"""
+from typing import List
+
+seive = [True] * 1000001
+i = 2
+while i * i <= 1000000:
+    if seive[i]:
+        for j in range(i * i, 1000001, i):
+            seive[j] = False
+    i += 1
+
+
+def is_prime(n: int) -> bool:
+    """
+    For 2 <= n <= 1000000, return True if n is prime.
+    >>> is_prime(87)
+    False
+    >>> is_prime(23)
+    True
+    >>> is_prime(25363)
+    False
+    """
+    return seive[n]
+
+
+def contains_an_even_digit(n: int) -> bool:
+    """
+    Return True if n contains an even digit.
+    >>> contains_an_even_digit(0)
+    True
+    >>> contains_an_even_digit(975317933)
+    False
+    >>> contains_an_even_digit(-245679)
+    True
+    """
+    return any(digit in "02468" for digit in str(n))
+
+
+def find_circular_primes(limit: int = 1000000) -> List[int]:
+    """
+    Return circular primes below limit.
+    >>> len(find_circular_primes(100))
+    13
+    >>> len(find_circular_primes(1000000))
+    55
+    """
+    result = [2]  # result already includes the number 2.
+    for num in range(3, limit + 1, 2):
+        if is_prime(num) and not contains_an_even_digit(num):
+            str_num = str(num)
+            list_nums = [int(str_num[j:] + str_num[:j]) for j in range(len(str_num))]
+            if all(is_prime(i) for i in list_nums):
+                result.append(num)
+    return result
+
+
+if __name__ == "__main__":
+    print(f"{len(find_circular_primes()) = }")