Python program to check whether a number is Prime or not
Given a positive integer N, The task is to write a Python program to check if the number is prime or not.
Definition: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are {2, 3, 5, 7, 11, ….}.
Examples :
Input: n = 11
Output: trueInput: n = 15
Output: falseInput: n = 1
Output: false
The idea to solve this problem is to iterate through all the numbers starting from 2 to (N/2) using a for loop and for every number check if it divides N. If we find any number that divides, we return false. If we did not find any number between 2 and N/2 which divides N then it means that N is prime and we will return True.
Below is the Python program to check if a number is prime:
Python3
# Python program to check if # given number is prime or not num = 11 # If given number is greater than 1 if num > 1 : # Iterate from 2 to n / 2 for i in range ( 2 , int (num / 2 ) + 1 ): # If num is divisible by any number between # 2 and n / 2, it is not prime if (num % i) = = 0 : print (num, "is not a prime number" ) break else : print (num, "is a prime number" ) else : print (num, "is not a prime number" ) |
11 is a prime number
Optimized Method
We can do the following optimizations:
Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of a smaller factor that has been already checked.
Now lets see the code for the first optimization method ( i.e. checking till √n )
Python3
from math import sqrt # n is the number to be check whether it is prime or not n = 1 # no lets check from 2 to sqrt(n) # if we found any facto then we can print as not a prime number # this flag maintains status whether the n is prime or not prime_flag = 0 if (n > 1 ): for i in range ( 2 , int (sqrt(n)) + 1 ): if (n % i = = 0 ): prime_flag = 1 break if (prime_flag = = 0 ): print ( "true" ) else : print ( "false" ) else : print ( "false" ) |
false
The algorithm can be improved further by observing that all primes are of the form 6k ± 1, with the exception of 2 and 3. This is because all integers can be expressed as (6k + i) for some integer k and for i = -1, 0, 1, 2, 3, or 4; 2 divides (6k + 0), (6k + 2), (6k + 4); and 3 divides (6k + 3). So a more efficient method is to test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1. (Source: wikipedia)