Next Prime Number

maths/next_prime_number.py

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+"""
+Next Prime Number -- https://en.wikipedia.org/wiki/Prime_number
+
+In the ancient city of Numeria,
+legends speak of an oracle whose whispers
+could bend the very fabric of mathematics.
+Travelers from distant lands would bring her a number,
+and in return, she would reveal its future:
+the very next prime number.
+Your task is to embody the oracle's wisdom.
+You will be given a number.
+You must find the smallest prime number
+that is strictly greater than it.
+"""
+
+
+def is_prime(number: int) -> bool:
+    """
+    Check if a number is prime.
+
+    >>> is_prime(2)
+    True
+    >>> is_prime(15)
+    False
+    >>> is_prime(19)
+    True
+    >>> is_prime(1)
+    False
+    >>> is_prime(-7)
+    False
+    """
+    if number <= 1:
+        return False
+    if number <= 3:
+        return True
+    if number % 2 == 0 or number % 3 == 0:
+        return False
+
+    factor = 5
+    while factor * factor <= number:
+        if number % factor == 0 or number % (factor + 2) == 0:
+            return False
+        factor += 6
+    return True
+
+
+def next_prime(number: int) -> int:
+    """
+    Find the smallest prime number strictly greater than the given number.
+
+    >>> next_prime(2)
+    3
+    >>> next_prime(7)
+    11
+    >>> next_prime(14)
+    17
+    >>> next_prime(0)
+    2
+    >>> next_prime(-10)
+    2
+    """
+    if not isinstance(number, int):
+        raise ValueError("next_prime() only accepts integral values")
+
+    candidate = number + 1
+    while not is_prime(candidate):
+        candidate += 1
+    return candidate
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    try:
+        n = int(input("Enter an integer: ").strip() or 0)
+        print(f"The next prime number after {n} is {next_prime(n)}")
+    except ValueError:
+        print("Please enter a valid integer.")