Check whether the given number is Wagstaff prime or not in Python

Suppose we have a number n. We have to check whether n is Wagstaff prime or not. As we know Wagstaff prime is a prime number which is in the following form.

where q is an odd prime number.

So, if the input is like n = 683, then the output will be True n can be represented as

So here q = 11. And q is odd prime.

To solve this, we will follow these steps −

• if num is prime and (num*3 - 1) is also prime, then
  • return True
• return False

Let us see the following implementation to get better understanding −

Example Code

def isPrime(num):
   if num > 1:
      for i in range(2, num):
         if num % i == 0:
           return False
      return True
   return False
   
def power_of_two(num):
   return num and not(num & (num - 1))

def solve(num) : 
   if isPrime(num) and power_of_two(num * 3-1): 
      return True
   return False

n = 683
print(solve(n))

Input

683

Output

True