# Find the XOR of first N Prime Numbers

Given a positive integer N, the task is to find the XOR of the first N prime numbers.

Examples:

Input: N = 3
Output: 4
First 3 prime numbers are 2, 3 and 5.
And 2 ^ 3 ^ 5 = 4

Input: N = 5
Output: 8

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

Approach:

1. Create Sieve of Eratosthenes to identify if a number is prime or not in O(1) time.
2. Run a loop starting from 1 until and unless we find N prime numbers.
3. XOR all the prime numbers and neglect those which are not prime.
4. Finally, print the XOR of the 1st N prime numbers.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define MAX 10000 ` ` `  `// Create a boolean array "prime[0..n]" and initialize ` `// all entries it as true. A value in prime[i] will ` `// finally be false if i is Not a prime, else true. ` `bool` `prime[MAX + 1]; ` `void` `SieveOfEratosthenes() ` `{ ` `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``prime = ``false``; ` ` `  `    ``for` `(``int` `p = 2; p * p <= MAX; p++) { ` ` `  `        ``// If prime[p] is not changed, then it is a prime ` `        ``if` `(prime[p] == ``true``) { ` ` `  `            ``// Set all multiples of p to non-prime ` `            ``for` `(``int` `i = p * 2; i <= MAX; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to return the xor of 1st N prime numbers ` `int` `xorFirstNPrime(``int` `n) ` `{ ` `    ``// Count of prime numbers ` `    ``int` `count = 0, num = 1; ` ` `  `    ``// XOR of prime numbers ` `    ``int` `xorVal = 0; ` ` `  `    ``while` `(count < n) { ` ` `  `        ``// If the number is prime xor it ` `        ``if` `(prime[num]) { ` `            ``xorVal ^= num; ` ` `  `            ``// Increment the count ` `            ``count++; ` `        ``} ` ` `  `        ``// Get to the next number ` `        ``num++; ` `    ``} ` `    ``return` `xorVal; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// Create the sieve ` `    ``SieveOfEratosthenes(); ` ` `  `    ``int` `n = 4; ` ` `  `    ``// Find the xor of 1st n prime numbers ` `    ``cout << xorFirstNPrime(n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach  ` `class` `GFG  ` `{ ` `static` `final` `int` `MAX = ``10000``; ` ` `  `// Create a boolean array "prime[0..n]"  ` `// and initialize all entries it as true.  ` `// A value in prime[i] will finally be false ` `// if i is Not a prime, else true.  ` `static` `boolean` `prime[] = ``new` `boolean` `[MAX + ``1``];  ` ` `  `static` `void` `SieveOfEratosthenes()  ` `{  ` `    ``int` `i ; ` `    ``for` `(i = ``0``; i < MAX + ``1``; i++) ` `    ``{ ` `        ``prime[i] = ``true``; ` `    ``} ` ` `  `    ``prime[``1``] = ``false``;  ` ` `  `    ``for` `(``int` `p = ``2``; p * p <= MAX; p++)  ` `    ``{  ` ` `  `        ``// If prime[p] is not changed,  ` `        ``// then it is a prime  ` `        ``if` `(prime[p] == ``true``)  ` `        ``{  ` ` `  `            ``// Set all multiples of p to non-prime  ` `            ``for` `(i = p * ``2``; i <= MAX; i += p)  ` `                ``prime[i] = ``false``;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Function to return the xor of  ` `// 1st N prime numbers  ` `static` `int` `xorFirstNPrime(``int` `n)  ` `{  ` `    ``// Count of prime numbers  ` `    ``int` `count = ``0``, num = ``1``;  ` ` `  `    ``// XOR of prime numbers  ` `    ``int` `xorVal = ``0``;  ` ` `  `    ``while` `(count < n) ` `    ``{  ` ` `  `        ``// If the number is prime xor it  ` `        ``if` `(prime[num])  ` `        ``{  ` `            ``xorVal ^= num;  ` ` `  `            ``// Increment the count  ` `            ``count++;  ` `        ``}  ` ` `  `        ``// Get to the next number  ` `        ``num++;  ` `    ``}  ` `    ``return` `xorVal;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main (String[] args)  ` `{  ` `    ``// Create the sieve  ` `    ``SieveOfEratosthenes();  ` ` `  `    ``int` `n = ``4``;  ` ` `  `    ``// Find the xor of 1st n prime numbers  ` `    ``System.out.println(xorFirstNPrime(n));  ` ` `  `}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

 `# Python3 implementation of the approach ` `MAX` `=` `10000` ` `  `# Create a boolean array "prime[0..n]" and  ` `# initialize all entries it as true.  ` `# A value in prime[i] will finally be false + ` `# if i is Not a prime, else true. ` `prime ``=` `[``True` `for` `i ``in` `range``(``MAX` `+` `1``)] ` ` `  `def` `SieveOfEratosthenes(): ` ` `  `    ``prime[``1``] ``=` `False` ` `  `    ``for` `p ``in` `range``(``2``, ``MAX` `+` `1``): ` ` `  `        ``# If prime[p] is not changed,  ` `        ``# then it is a prime ` `        ``if` `(prime[p] ``=``=` `True``): ` ` `  `            ``# Set all multiples of p to non-prime ` `            ``for` `i ``in` `range``(``2` `*` `p, ``MAX` `+` `1``, p): ` `                ``prime[i] ``=` `False` ` `  `# Function to return the xor of  ` `# 1st N prime numbers ` `def` `xorFirstNPrime(n): ` `     `  `    ``# Count of prime numbers ` `    ``count ``=` `0` `    ``num ``=` `1` ` `  `    ``# XOR of prime numbers ` `    ``xorVal ``=` `0` ` `  `    ``while` `(count < n): ` ` `  `        ``# If the number is prime xor it ` `        ``if` `(prime[num]): ` `            ``xorVal ^``=` `num ` ` `  `            ``# Increment the count ` `            ``count ``+``=` `1` ` `  `        ``# Get to the next number ` `        ``num ``+``=` `1` ` `  `    ``return` `xorVal ` ` `  `# Driver code ` ` `  `# Create the sieve ` `SieveOfEratosthenes() ` ` `  `n ``=` `4` ` `  `# Find the xor of 1st n prime numbers ` `print``(xorFirstNPrime(n)) ` ` `  `# This code is contributed by Mohit Kumar `

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `static` `int` `MAX = 10000; ` ` `  `// Create a boolean array "prime[0..n]"  ` `// and initialize all entries it as true.  ` `// A value in prime[i] will finally be false ` `// if i is Not a prime, else true.  ` `static` `bool` `[]prime = ``new` `bool` `[MAX + 1];  ` ` `  `static` `void` `SieveOfEratosthenes()  ` `{  ` `    ``int` `i ; ` `    ``for` `(i = 0; i < MAX + 1; i++) ` `    ``{ ` `        ``prime[i] = ``true``; ` `    ``} ` ` `  `    ``prime = ``false``;  ` ` `  `    ``for` `(``int` `p = 2; p * p <= MAX; p++)  ` `    ``{  ` ` `  `        ``// If prime[p] is not changed,  ` `        ``// then it is a prime  ` `        ``if` `(prime[p] == ``true``)  ` `        ``{  ` ` `  `            ``// Set all multiples of p to non-prime  ` `            ``for` `(i = p * 2; i <= MAX; i += p)  ` `                ``prime[i] = ``false``;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Function to return the xor of  ` `// 1st N prime numbers  ` `static` `int` `xorFirstNPrime(``int` `n)  ` `{  ` `    ``// Count of prime numbers  ` `    ``int` `count = 0, num = 1;  ` ` `  `    ``// XOR of prime numbers  ` `    ``int` `xorVal = 0;  ` ` `  `    ``while` `(count < n) ` `    ``{  ` ` `  `        ``// If the number is prime xor it  ` `        ``if` `(prime[num])  ` `        ``{  ` `            ``xorVal ^= num;  ` ` `  `            ``// Increment the count  ` `            ``count++;  ` `        ``}  ` ` `  `        ``// Get to the next number  ` `        ``num++;  ` `    ``}  ` `    ``return` `xorVal;  ` `}  ` ` `  `// Driver code  ` `static` `public` `void` `Main () ` `{ ` `     `  `    ``// Create the sieve  ` `    ``SieveOfEratosthenes();  ` `    ``int` `n = 4;  ` ` `  `    ``// Find the xor of 1st n prime numbers  ` `    ``Console.Write(xorFirstNPrime(n));  ` `}  ` `} ` ` `  `// This code is contributed by Sachin `

Output:
```3
```

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