Check whether N is a Dihedral Prime Number or not in Python

Suppose we have a number n. We have to check whether n is dihedral prime or not. A number is said to be dihedral prime when that number is itself prime and also shown same number or any other prime number using 7-segment display regardless the orientation of the display (normal or up-side down).

So, if the input is like n = 1181, then the output will be True

second one is up-side down format of the first one and both are prime.

To solve this, we will follow these steps −

• Define a function up_side_down() . This will take n
• temp := n, total := 0
• while temp > 0, do
  • d := temp mod 10
  • if d is same as 2, then d := 5
  • otherwise when d is same as 5, then d := 2
  • total := total * 10 + d
  • temp := quotient of (temp / 10)
• return total
• From the main method do the following:
• if n is not prime or up_side_down(n) is not prime or reverse of n is not prime or reverse of up_side_down(n) is not prime, then
  • return False
• temp := n
• while temp > 0, do
  • rem := temp mod 10
  • if rem is any of these [3, 4, 6, 7, 9], then
    • return False
  • temp := quotient of (temp / 10)
• return True

Let us see the following implementation to get better understanding −

Example Code

prime = (int(1e5)+5)*[True]
def reverse(n):
   return int(str(n)[::-1])
 
def up_side_down(n):
   temp = n
   total = 0
   while temp>0:
      d = temp % 10
      if d == 2:
         d = 5
      elif d == 5:
         d = 2
      total = total * 10 + d
      temp//= 10
 
   return total
 
def get_all_prime():
   prime[0] = prime[1] = False
 
   for i in range(2, int(1e5)+1):
      j = 2
      while i * j<= int(1e5):
         prime[i * j] = False
         j+= 1
 
def solve(n):
   get_all_prime()
   if not prime[n] or not prime[up_side_down(n)] or not prime[reverse(n)] or not prime[reverse(up_side_down(n))]:
      return False
 
   temp = n
 
   while temp>0:
      rem = temp % 10;
      if rem in [3, 4, 6, 7, 9]:
         return False
      temp //= 10
 
   return True

n = 1181
print(solve(n))

Input

23, 3

Output

True