# Pernicious number

A pernicious number is a positive integer which has prime number of ones in its binary representation. The first pernicious number is 3 since 3 = (11)(in binary representation) and 1 + 1 = 2, which is a prime.

Properties of Pernicious Numbers :

1. There isn’t any pernicious number which is also power of 2 because powers of two in binary form are represented as a one followed by zeros. So, 1 is not considered as a prime number.
2. Every number of the form + 1 with n > 0 is a pernicious number as the number of ones in binary form is 2 which is prime.
3. A number of the form – 1 with prime p is a pernicious number known as a Mersenne number .

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea to print first n Pernicious numbers is simple.

Do following for every number from 1 to n.
1) Count set bits in current number
2) Print current number if count of set bits is prime. We use simple primality check for this purpose.

Here is the program to print first 25 pernicious number.

Below is the implementation of the above approach.

## C++

 `// CPP program to print first n pernicious numbers ` `#include ` `using` `namespace` `std; ` ` `  `// function to check prime number ` `bool` `isPrime(``int` `x) ` `{ ` `    ``if` `(x < 2) ` `        ``return` `false``; ` `    ``for` `(``int` `i = 2; i < x; i++) { ` `        ``if` `(x % i == 0) ` `            ``return` `false``; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Prints first n Pernicious numbers ` `void` `printPernicious(``int` `n) ` `{ ` `    ``for` `(``int` `i=1,count=0; count

## Java

 `// Java program to print first ` `// n pernicious numbers ` `import` `java.util.*; ` ` `  `class` `GFG { ` `    ``// function to count no of ` `    ``// ones in binary representation ` `    ``static` `int` `countSetBits(``int` `n) ` `    ``{ ` `        ``int` `count = ``0``; ` `         `  `        ``while` `(n > ``0``) ` `        ``{ ` `            ``n &= (n - ``1``) ; ` `            ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` `     `  `    ``// function to check prime number ` `    ``static` `boolean` `isPrime(``int` `x) ` `    ``{ ` `        ``if` `(x < ``2``) ` `            ``return` `false``; ` `        ``for` `(``int` `i = ``2``; i < x; i++) { ` `            ``if` `(x % i == ``0``) ` `                ``return` `false``; ` `        ``} ` `        ``return` `true``; ` `    ``} ` `     `  `    ``// Prints first n Pernicious numbers ` `    ``static` `void` `printPernicious(``int` `n) ` `    ``{ ` `        ``for` `(``int` `i=``1``,count=``0``; count

## Python3

 `# Python program to print ` `# first n pernicious numbers ` ` `  `# function to check  ` `# prime number ` `def` `isPrime(x): ` `     `  `    ``if` `x < ``2``:  ` `        ``return` `False` `     `  `    ``for` `i ``in` `range``(``2``, x): ` `        ``if` `not` `x ``%` `i:  ` `            ``return` `False` `     `  `    ``return` `True` ` `  `# Prints first n Pernicious ` `# numbers ` `def` `printPernicious(n): ` ` `  `    ``i, count ``=` `1``, ``0` ` `  `    ``while` `count < n: ` ` `  `        ``# "bin(i).count('1')" count ` `        ``# no of ones in binary  ` `        ``# representation ` `        ``if` `(isPrime(``bin``(i).count(``'1'``))): ` `            ``print``(i, end``=``' '``) ` `            ``count ``+``=` `1` `         `  `        ``i ``+``=` `1` ` `  `# Driver Code ` `n ``=` `25` `printPernicious(n) ` ` `  `# This code is contributed by Ansu Kumari `

## C#

 `// C#program to print first ` `// n pernicious numbers ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``// function to count no of ` `    ``// ones in binary representation ` `    ``static` `int` `countSetBits(``int` `n) ` `    ``{ ` `        ``int` `count = 0; ` `         `  `        ``while` `(n > 0) ` `        ``{ ` `            ``n &= (n - 1) ; ` `            ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` `     `  `    ``// function to check prime number ` `    ``static` `bool` `isPrime(``int` `x) ` `    ``{ ` `        ``if` `(x < 2) ` `            ``return` `false``; ` `        ``for` `(``int` `i = 2; i < x; i++) { ` `            ``if` `(x % i == 0) ` `                ``return` `false``; ` `        ``} ` `        ``return` `true``; ` `    ``} ` `     `  `    ``// Prints first n Pernicious numbers ` `    ``static` `void` `printPernicious(``int` `n) ` `    ``{ ` `        ``for` `(``int` `i=1,count=0; count

## PHP

 `> 1; ` `    ``} ` ` `  `    ``return` `\$count``; ` `} ` ` `  `// Prints first n Pernicious numbers ` `function` `printPernicious(``\$n``) ` `{ ` `    ``for` `(``\$i` `= 1, ``\$count` `= 0;  ` `                ``\$count` `< ``\$n``; ``\$i``++)  ` `    ``{ ` ` `  `        ``//count no of ones in  ` `        ``// binary representation ` `        ``if` `(isPrime(getBitCount(``\$i``)))  ` `        ``{ ` `            ``echo` `\$i``.``" "``; ` `             `  `            ``\$count``++; ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code ` `\$n` `= 25; ` `printPernicious(``\$n``); ` ` `  `// This code is contributed by mits  ` `?> `

Output :

```3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22 24 25 26 28 31 33 34 35 36
```

References :
Wiki

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Improved By : Mithun Kumar