CareerCup

#include<bits/stdc++.h>
using namespace std;
int prime(int n)
{
int flag=0,i;
for(i=2;i<=sqrt(n);i++)
{
if(n%i==0)
flag=1;
}
if(flag==0)
return 0;
}
int main()
{
int a,i=0,j,k,n,b;
cin>>a;
cin>>n;
while(i<=n)
{
b=++a;
j=prime(b);
if(j==0)
i++;
if(i==5){
cout<<b;
break;
}
a=b;

}
}

C++, Caching

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

vector<int> primes;

void initPrime(int a) {
	int i, j, l;
	bool p;

	for (i = 2; i <= a; i++) {
		l = (int)sqrt((double)i);
		p = true;
		for (j = 0; j < primes.size(); j++) {
			if (l < primes[j]) break;
			if (i % primes[j] == 0) {
				p = false;
				break;
			}
		}
		if (p) primes.push_back(i);
	}
}

bool isPrime(int n) {
	int i, l;

	if (n < 2) return false;

	l = (int)sqrt((double)n);
	for (i = 0; i < primes.size(); i++) {
		if (l < primes[i]) break;
		if (n % primes[i] == 0) return false;
	}
	primes.push_back(n);

	return true;
}

int solve(int a, int n) {
	initPrime(a);

	while (n) {
		if (isPrime(++a)) n--;
	}

	return a;
}

int main(int argc, char* argv[]) {
	int a, n;

	cin >> a >> n;
	cout << solve(a, n) << "\n";

	return 0;
}

Java code:

public class PrimeNumber {
	
	public void print(int a, int n) {
		while (n != 0) {
			if (isPrime(++a)) {
				--n;
			}
		}
		System.out.println(a);
	}
	
	private boolean isPrime(int a) {
		if (a == 2) {
			return true;
		} else if(a < 2 || a % 2 == 0) {
			return false;
		}
		for (int i = 3; i*i <= a; i += 2) {
			if (a % i == 0) {
				return false;
			}
		}
		return true;
	}
	
}

Quadratic time, constant space complexity. If we have maximum limit for output prime number, we could use Sieve of Eratosthenes to calculate all prime numbers beforehand. Thus, complexity would be O(n log log n) time and O(N) space.

A prime number could be in format of 6n+-1 so check for numbers in this format if they are prime or not upto the given count.

int c = 0;
	int n = 1;
	int lastPrime=-1;
	while( c < N ) {
		int k1 = 6*n-1;
		int k2 = 6*n +1;
		if( isPrime(k1) )	{ lastPrime = k1; c++; }
		if(c == N)	break;
		if(isPrime(k2) )		{ lastPrime = k2; c++; }
		n++;
	}
	return lastPrime;

<?php

$handle = fopen ("php://stdin","r");
fscanf($handle,"%d",$n);
//var_dump($n);
for($i=1;;$i++)
{ $n=$n+1;
// var_dump($n);
if($n%2!=0){
$p[]=$n;
if(count($p)==5)
break;
}
}
var_dump(end($p));

<?php

$handle = fopen ("php://stdin","r");
fscanf($handle,"%d",$n);
//var_dump($n);
for($i=1;;$i++)
    {  $n=$n+1;
    // var_dump($n);
      if($n%2!=0){
          $p[]=$n;
         if(count($p)==5)
             break;
          }    
}
var_dump(end($p));