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Count of primes after converting given binary number in base between L to R
  • Last Updated : 30 Jul, 2020

Given a binary number N, and a range represented by L, and R, the task is to convert the given binary number in all the base numbers between L and R (L and R inclusive) and count the resulting prime numbers among them.

Examples:

Input: N = 111, L = 3, R = 10
Outpu: 5
Explanation:
When 111 is interpreted in all the base numbers between 3 and 10 we get the resulting numbers as [21, 13, 12, 11, 10, 7, 7, 7], out of which only 5 numbers are prime. Hence, the output is 5.

Input: N = 11, L = 4, R = 19
Output: 16
Explanation:
When 11 is interpreted in all the base numbers between 4 and 19 we get the resulting numbers as 3 which is a prime number. Hence, the output is 16.

Approach: Convert the given binary number to each base between ‘L’ and ‘R’ one by one. Thereafter, check if the resulting number is prime or not. If yes, then increment the count.



Below is the implementation of the above approach:




# Python3 program to count of primes
# after converting given binary
# number in base between L to R
  
# Function to interpret the binary number in all
# the base numbers between L and R one by one 
def calc(binary, interpret_language):
      
    # Temporary integer as intermediate
    # value in a known language
    tmp = 0
      
    # Represenation of digits in base 2
    base = "01" 
      
    # For each digit in the 'binary'
    # get its index and its value
    for n, digit in enumerate(binary[::-1]):
        tmp += base.index(digit)*len(base)**n
          
    # Generate the 'resulting_number' by appending
    resulting_number = ''
      
    while tmp:
        resulting_number += interpret_language[tmp % len(interpret_language)]
          
        # reduce the value of tmp
        tmp //= len(interpret_language) 
          
    return resulting_number
  
# Function to check if the resulting 
# number is prime or not
def IS_prime (N):
    n = int(N)
    c = 1
      
    for i in range (2, n + 1):
        if (n % i == 0):
            c+= 1
              
    if (c == 2):
        return 1
          
    return 0
      
# Driver program
if __name__ == '__main__'
    binary = "111" 
    L = 3
    R = 10
    bases = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 'A', 'B', 'D',
            'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M'
            'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U',
            'V', 'W', 'X', 'Y', 'Z']
  
    b = bases[0:R]
      
    # Count all the resulting numbers which are prime 
    count = 0
      
    for i in range (R-L + 1):
          
        # 'list' indicates representation of digits 
        # in each base number 
        list = b[:(L + i)] 
          
        # Converting in string
        interpret_language = ''.join(map(str, list))
          
        # Converting the binary number to the respective 
        # base between L and R
        resulting_number = calc(binary, interpret_language)
        if(IS_prime(resulting_number) == 1):
            count+= 1
              
    print (count)
Output:
5

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