How to Check if a Number is Prime in Python

The fastest way to check if a number is prime in Python is dividing only up to its square root:

import math

def es_primo(n):
    if n < 2:
        return False
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

When do you need this?

A prime number is only divisible by 1 and by itself. Checking primes is a classic exercise in Python and a common question in technical interviews. You will also find it in cryptography, random number generation and math exercises. In this guide you will learn how to check if a number is prime in Python, from a simple loop to an optimized algorithm.

Method 1: Check with a simple loop

The most direct way is to try dividing the number by every value from 2 to n - 1.

def es_primo(n):
    if n < 2:
        return False
    for i in range(2, n):
        if n % i == 0:
            return False
    return True

print(es_primo(7))   # True
print(es_primo(10))  # False

You only need to check divisors up to the square root of n. If none of them divides n, the number is prime. This makes the function much faster.

import math

def es_primo(n):
    if n < 2:
        return False
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

Method 3: Optimize with the 6k ± 1 rule

For large numbers you can skip even numbers and multiples of 3. Every prime greater than 3 has the form 6k - 1 or 6k + 1.

def es_primo(n):
    if n < 2:
        return False
    if n in (2, 3):
        return True
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

Method comparison

Method Advantage When to use it
Simple loop Easy to understand Learning and small numbers
Square root Fast for most cases Recommended in general
6k ± 1 rule Very fast Large numbers and contests

Special cases and common errors

Remember to handle the special cases before anything else:

  • Numbers less than 2 are not prime.
  • 2 is the only even prime number.
  • 0 and 1 are not prime.
print(es_primo(1))   # False
print(es_primo(2))   # True
print(es_primo(0))   # False

Frequently asked questions

Is 1 a prime number?

No. A prime number must be greater than 1.

Is 2 a prime number?

Yes. 2 is the smallest prime number and the only even prime.

What is the fastest way to check primality in Python?

For most cases, the square root optimization is enough. For very large numbers you can use the 6k ± 1 rule or specialized libraries.

Related content

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