What’s actually slowing this PC down?
Pick the symptom - the matching free tool is one click away.
Use a function that returns True when an integer is prime and False otherwise. This version rejects values below 2 and tests divisors only through the exact integer square root.
Python prime-number program using a function
from math import isqrt
def is_prime(n):
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")For example, entering 9 prints 9 is not prime; entering 7 prints 7 is prime. The examples follow directly from the function’s logic.
As an Amazon Associate I earn from qualifying purchases.
How the function decides whether a number is prime
Reject numbers below 2
A prime is an integer greater than 1 whose only positive divisors are 1 and itself. The first condition handles zero, one, and negative integers before the loop. Without it, the loop might not run for a small input, and the function could incorrectly reach return True.
Test divisibility with the remainder operator
For an integer candidate divisor, n % divisor == 0 means the division leaves no remainder. Python defines % as the operator that yields the remainder from dividing the first argument by the second (Python language reference).
#1 Best Overall
Stop at the square root, including the endpoint
If a number has a factor greater than its square root, it must also have a paired factor below the square root. So it is enough to test divisors from 2 through that boundary. Python’s range excludes its stop value, which is why the code uses isqrt(n) + 1 as the stop.
math.isqrt returns the floor of the exact square root for a nonnegative integer and has been available since Python 3.8, according to the Python 3.14.8 math documentation. Using it avoids relying on a floating-point square root for the loop bound.
What happens with small inputs and perfect squares
2and3pass: neither has a candidate divisor in the loop.4fails at divisor 2.9fails at divisor 3. Adding 1 to the range stop ensures the square-root endpoint is tested.1and negative integers returnFalseimmediately.
A common boundary bug is writing range(2, int(n ** 0.5)). Since the stop is excluded, that form can skip the square root itself—for example, divisor 3 for 9. The explicit inclusive bound in the program avoids that error.
The Tool Desk
Outbyte Driver Updater FREEFix the driver behind crashes, sound loss and screen glitchesFind Drivers →Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Why the function returns a Boolean
is_prime(n) answers the calculation by returning a Boolean. The input and print statements handle interaction separately, so other code can call the function without printing from inside it. When a divisor is found, return False ends the search immediately; if the loop finishes without finding one, the number is prime.
When to use a different prime-number method
One number: trial division
This function uses trial division, a readable choice when the task is to classify one integer. Its square-root bound reduces the number of checks, but trial division becomes impractical for extremely large integers.
Every prime up to a limit: a sieve
If the goal is to generate all primes up to a maximum, use a Sieve of Eratosthenes rather than calling this function for every candidate. A sieve marks composite numbers across the range and collects the unmarked values; Al Sweigart’s chapter on finding and generating prime numbers presents this approach for range generation.
Very large integers
For extremely large values, the same chapter introduces Rabin–Miller testing rather than suggesting trial division scales indefinitely. The classroom function is for straightforward integer checks; it does not establish cryptographic suitability.
Further reading
Al Sweigart’s Cracking Codes with Python includes a chapter on testing and generating prime numbers, with trial-division and sieve approaches: Finding and Generating Prime Numbers.
Quick Recap
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
