# Count of primes after converting given binary number in base between L to R

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 = 10Output:5Explanation:

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 = 19Output:16Explanation:

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.

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**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

`# 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)` |

**Output:**

5