Python isprime – Function for Determining if Number is Prime

Finding out if a number is prime is easy to do in Python. We can determine if a number is prime if it has no factors between 2 and the square root of the number.

Below is a function which will determine if a number is prime in Python.

def isPrime(n):
    if (n <=  1):
        return False
    if (n % 2 == 0):
        return False
    for i in range(3, int(n**0.5 + 1), 2):
        if (n % i == 0):
            return False
    return True

When working with numbers, sometimes it can be useful to know if a number is prime or not.

We can find if a number is prime easily in Python with the help of the division method for prime factorization.

To determine if a number is a prime number, we need that only the number and 1 can divide the number. To check this, we need to do the following:

First, if the given number is even, then we know that 2 divides the number and the number is not prime.

Next, we need to loop through the odd numbers 3 until the square root of the number to see if there are any numbers which can divide our number.

Why are we doing this?

First, we only need to check odd numbers because if the number is even, then the function will have returned “False” in the first step. Second, we only need to check until the square root of the temporary number because of the statement: Every composite number has at least one prime factor less than or equal to the square root of itself.

Below is the final function to find out if a number if a prime number using Python.

def isPrime(n):
    if (n <=  1):
        return False
    if (n % 2 == 0):
        return False
    for i in range(3, int(n**0.5 + 1), 2):
        if (n % i == 0):
            return False
    return True

Determining if a Number is Prime Using Python

We can now use our function for seeing if a number is a prime number to determine if various numbers or primes or not.

Let’s look and see if there are primes for a handful of numbers in the following example.

def isPrime(n):
    if (n <=  1):
        return False
    if (n % 2 == 0):
        return False
    for i in range(3, int(n**0.5 + 1), 2):
        if (n % i == 0):
            return False
    return True
        
print(isPrime(10))
print(isPrime(13))
print(isPrime(90))
print(isPrime(121))
print(isPrime(749))
print(isPrime(283))

#Output:
False
True
False
False
False
True

Finding the First n Primes in Python

Let’s use our isPrime() function to find the first n primes, given n, in Python.

To find the first n primes, we will loop from 2 until we have n primes.

Below is a Python function which will return the first n primes.

def getPrimes(n):
    primes = [2]
    num = 3
    while (len(primes) < n):
        if(isPrime(num)):
            primes.append(num)
        num = num + 2
    return primes

For example, if we want to find the first 10 prime numbers, we can do so in the following Python code.

def getPrimes(n):
    primes = [2]
    num = 3
    while (len(primes) < n):
        if(isPrime(num)):
            primes.append(num)
        num = num + 2
    return primes

#Output:
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

If we want to find the first 20 prime numbers, we can call our function with 20.

def getPrimes(n):
    primes = [2]
    num = 3
    while (len(primes) < n):
        if(isPrime(num)):
            primes.append(num)
        num = num + 2
    return primes

#Output:
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

Hopefully this article has been useful for you to learn how to determine if a number is prime in Python.