Check Prime Number in Python

Last Updated : 16 May, 2026

Given a positive integer n, the task is to check whether the number is prime or not in Python. A prime number is a number greater than 1 that has exactly two factors, 1 and itself. For Example:

Input: n = 29
Output: Prime Number

Input: n = 10
Output: Not a Prime Number

Let’s look at the methods below to check for a prime number.

Using flag variable

The program checks whether the number is divisible by any value from 2 to √n. If any divisor is found, the number is not prime; otherwise, it is prime.

Python 
n = 11
if n <= 1:
    print(False)
else:
    prime = True

    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            prime = False
            break
    print(prime)

Output
True

Explanation:

  • n <= 1 checks numbers that are not prime. Loop runs from 2 to √n.
  • n % i == 0 checks divisibility and prime becomes False if a divisor is found.

Using isprime() method

This method uses the isprime() function from the SymPy library to check whether a number is prime.

Python 
from sympy import isprime
n = 13
print(isprime(n))

Output

True

Explanation:

  • isprime(n) checks whether n is prime.
  • Function returns True for prime numbers and False otherwise.

Using Sieve of Eratosthenes

This method creates a list of numbers and marks multiples of each number as non-prime until the target number is reached.

Python 
def is_prime(n):
    if n < 2:
        return False

    s = [True] * (n + 1)
    s[0] = s[1] = False

    for i in range(2, int(n**0.5) + 1):
        if s[i]:
            for j in range(i * i, n + 1, i):
                s[j] = False
    return s[n]

print(is_prime(31))

Output
True

Explanation:

  • s stores prime status of numbers.
  • Multiples of each number are marked False.
  • s[n] determines whether the number is prime.

Using Recursion

This approach checks divisibility recursively by reducing the divisor value in each function call.

Python 
from math import sqrt

def prime(n, i):
    if i == 1:
        return True
    if n % i == 0:
        return False
    return prime(n, i - 1)

n = 13
print(prime(n, int(sqrt(n))))

Output
True

Explanation:

  • Function checks whether n is divisible by i. If divisible, it returns False.
  • Otherwise, recursion continues with i - 1. If no divisor is found, it returns True.
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