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POPrime generating number finder not producing correct output
 

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  1. POPrime generating number finder not producing correct output
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    <p>I'm working on this problem:</p> <blockquote> <p>Consider the divisors of 30: 1,2,3,5,6,10,15,30.<br> It can be seen that for every divisor d of 30, d+30/d is prime.</p> <p>Find the sum of all positive integers n not exceeding 100 000 000 such that for every divisor d of n, d+n/d is prime.</p> </blockquote> <p>and I thought for sure I had it, but alas, it's apparently giving me the wrong answer (<code>12094504411074</code>).</p> <p>I am fairly sure my sieve of Eratosthenes is working (but maybe not), so I think the problem is somewhere in my algorithm. It seems to get the right answer for <code>n = 30</code> (<code>1+2+6+10+22+30 = 71</code> - is this correct?), but as numbers get larger, it apparently stops working.</p> <p>Here is my Java code:</p> <pre><code>import java.util.HashSet; public class Generators { static HashSet&lt;Integer&gt; hSet = new HashSet&lt;Integer&gt;(); public static void main(String[] args) { // TODO Auto-generated method stub int n = 100000000; sieveErat(n + 1); //Fill a hashSet with prime numbers System.out.println("Sieve complete"); int check = 0; long sum = 3; for(int i = 2; i &lt;= n; i++){ int numDivisors = 0; int numPrimeChecks = 0; boolean done = false; if(!hSet.contains(i+1)){ //i+1 must be a prime number for i to be prime generating continue; } else{ for(int j = 2; j &lt; i/2; j++){ if(i%j == 0){ numDivisors++; check = j + i/j; if(hSet.contains(check)){ done = true; numPrimeChecks++; } }else{ break; } } if(numPrimeChecks == numDivisors &amp;&amp; done){ sum += i; } } } System.out.println(sum); } public static void sieveErat(int N){ boolean[] isPrime = new boolean[N + 1]; for (int i = 2; i &lt;= N; i++) { isPrime[i] = true; //count++; } // mark non-primes &lt;= N using Sieve of Eratosthenes for (int i = 2; i*i &lt;= N; i++) { // if i is prime, then mark multiples of i as nonprime // suffices to consider mutiples i, i+1, ..., N/i if (isPrime[i]) { for (int j = i; i*j &lt;= N; j++) { isPrime[i*j] = false; // count--; } } } for(int i = 2; i &lt; isPrime.length; i++){ if(isPrime[i]){ hSet.add(i); } } // System.out.println(count); } } </code></pre>
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