Prime numbers play a central role in many e it applications like cryptography. So it is a necessity to check for prime numbers using Python programs in various applications. A prime number is a number which doesn't have any factors other than one and itself. Below will see programs that can find out if a given number is prime or not.
Approach
We take the following approach to decide whether a number is prime or not.
Check at the beginning is positive or not. As only positive numbers can be prime numbers.
We divide the number with all the numbers in the range of 2 to one number less than given number.
If the remainder becomes zero for any number in this range then it is not a prime number.
Example
x = 23 if x > 1: for n in range(2, x): if (x % n) == 0: print(x, "is not prime") print(n, "times", x // n, "is", x) break else: print(x, "is a prime number") else: print(x, "is not prime number")
Output
Running the above code gives us the following result −
23 is a prime number
Checking for the form 6i+1
All prime numbers which are greater than 6 can be represented in the form of 6i+1. Here I starts from 1 and goes on as integer. In the below example we will check if the number can be presented in the form of 6i+1 by dividing its 6 and checking for a reminder as one. Accordingly, will decide if the number is prime or not. Also we need to check for a i value which is equal to square root of the given number.
Example
def CheckPrime(n):
# Check for cases of 2 and 3
if (n <= 1):
return False
if (n <= 3):
return True
# skip checking middle five numbers in the 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
# Check for inputs
if (CheckPrime(31)):
print(" true")
else:
print(" false")
if (CheckPrime(25)):
print(" true")
else:
print(" false")Output
Running the above code gives us the following result −
true false