Python Program to Check Prime Number

Given a positive integer, check if the number is prime or not. A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of first few prime numbers are {2, 3, 5,

Examples:

Input:  n = 11
Output: true

Input:  n = 15
Output: false

Input:  n = 1
Output: false

School Method :

# A school method based Python3
# program to check if a number
# is prime

def isPrime(n):

    # Corner case
    if n <= 1:
        return False

    # Check from 2 to n-1
    for i in range(2, n):
        if n % i == 0:
            return False;

    return True

# Driver Program to test above function
print("true") if isPrime(11) else print("false")
print("true") if isPrime(14) else print("false")

# This code is contributed by Smitha Dinesh Semwal

Output:

true
false

Time complexity of this solution is O(n)

Optimized School Method :

# A optimized school method based
# Python3 program to check
# if a number is prime


def isPrime(n) :
    # Corner cases
    if (n <= 1) :
        return False
    if (n <= 3) :
        return True

    # This is checked so that we can skip
    # middle five numbers in below loop
    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 = i + 6

    return True


# Driver Program

if(isPrime(11)) :
    print(" true")
else :
    print(" false")

if(isPrime(15)) :
    print(" true")
else :
    print(" false")


# This code is contributed
# by Nikita Tiwari.

Output:

true
false

Please refer complete article on Primality Test | Set 1 (Introduction and School Method) for more details!