在 L 到 R 之间转换给定二进制数后的素数计数

给定一个二进制数N ，以及一个由L和R表示的范围，任务是将给定的二进制数转换为 L 和 R 之间(包括 L 和 R 在内)的所有基数，并计算其中产生的质数。
例子：

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. 
 

方法：将给定的二进制数一一转换为’L’和‘R’之间的每个基数。此后，检查结果数字是否为素数。如果是，则增加计数。
下面是上述方法的实现：

Python3

# 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
     
    # Representation 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)

输出：

5