Add emirp number detection algorithm

maths/emirp_check.py

@@ -0,0 +1,124 @@
+"""
+An emirp (prime spelled backwards) is a prime number that results in a different
+prime when its digits are reversed. This means that the number is not a
+palindromic prime.
+
+For more information about emirp numbers, refer to:
+https://en.wikipedia.org/wiki/Emirp
+"""
+
+
+def is_prime(number: int) -> bool:
+    """
+    Check if a number is prime.
+
+    Args:
+        number: A positive integer.
+
+    Returns:
+        True if the number is prime, False otherwise.
+
+    Raises:
+        ValueError: If number is not a positive integer.
+
+    Examples:
+        >>> is_prime(2)
+        True
+        >>> is_prime(3)
+        True
+        >>> is_prime(4)
+        False
+        >>> is_prime(9679)
+        True
+        >>> is_prime(1)
+        False
+        >>> is_prime(0)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> is_prime(-1)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> is_prime(2.5)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> is_prime("2")
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+    """
+    if not isinstance(number, int) or number <= 0:
+        raise ValueError("Input must be a positive integer.")
+
+    if 1 < number < 4:
+        return True
+    elif number < 2 or (number % 2 == 0):
+        return False
+
+    # Return True if number is not divisible by any odd number up to its square root
+    return all(number % i != 0 for i in range(3, int(number**0.5) + 1, 2))
+
+
+def emirp_check(number: int) -> bool:
+    """
+    Check if a number is an emirp number.
+
+    Args:
+        number: A positive integer.
+
+    Returns:
+        True if the number is an emirp number, False otherwise.
+
+    Raises:
+        ValueError: If number is not a positive integer.
+
+    Examples:
+        >>> emirp_check(13)
+        True
+        >>> emirp_check(23)
+        False
+        >>> emirp_check(9679)
+        True
+        >>> emirp_check(5)
+        False
+        >>> emirp_check(0)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> emirp_check(-13)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> emirp_check(1.9)
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> emirp_check("cat")
+        Traceback (most recent call last):
+            ...
+        ValueError: Input must be a positive integer.
+        >>> emirp_check(17)
+        True
+        >>> emirp_check(31)
+        True
+        >>> emirp_check(79)
+        True
+        >>> emirp_check(101)
+        False
+    """
+    if not isinstance(number, int) or number <= 0:
+        raise ValueError("Input must be a positive integer.")
+
+    if is_prime(number):
+        reversed_number = int(str(number)[::-1])
+        if number != reversed_number and is_prime(reversed_number):
+            return True
+    return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()