To check whether an integer is prime in Python, reject values below 2, then test possible divisors from 2 through the integer square root. If any divisor divides evenly, the number is not prime; otherwise, it is prime.
Python code to check a prime number
This function uses Python’s standard-library math.isqrt function to get an exact integer loop limit:
from math import isqrt
def is_prime(n: int) -> bool:
if n < 2:
return False
for divisor in range(2, isqrt(n) + 1):
if n % divisor == 0:
return False
return True
number = int(input("Enter an integer: "))
if is_prime(number):
print(f"{number} is prime")
else:
print(f"{number} is not prime")The code expects an integer as input. For example, entering 17 prints 17 is prime; entering 18 prints 18 is not prime. If the input is text that cannot be converted to an integer, int() raises ValueError.
Why the test stops at the square root
A prime number is an integer greater than 1 whose only positive divisors are 1 and itself. Negative integers, 0, and 1 are not prime, which is why the function returns False for every n < 2.
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For values of 2 or more, a divisor greater than the square root would have a matching factor smaller than the square root. The loop would find that smaller factor first, so checking past the square root is unnecessary. The math.isqrt function returns the floor of the exact square root of a nonnegative integer, as described in the Python math documentation.
What the loop checks
n % divisor == 0means the division has no remainder, so the number is composite and the function returnsFalse.range(2, isqrt(n) + 1)starts at 2. Python excludes the stop value inrange, so adding 1 includes the integer square-root bound when it is a whole number.- If the loop finishes without finding a divisor, the function returns
True.
The number 2 works without a special case: its divisor range is empty, so the function reaches return True.
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Python version and alternatives
math.isqrt was added in Python 3.8. This exact example therefore requires Python 3.8 or later. The method is a clear trial-division test for one number; it is not presented as an optimal approach for cryptographic-scale integers.
If the task is to find every prime up to a maximum rather than test one value, that is a different problem. A sieve may be more suitable for that task, though no particular runtime or memory advantage is established here. For official learning resources, see the Python Software Foundation’s documentation index.
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