Check Prime Number in Python (original) (raw)

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)

**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))

**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))))

**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.

Check Prime Number in Python (original) (raw)

Using flag variable

Using isprime() method

Using Sieve of Eratosthenes

Using Recursion

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