Project Euler(50)

Posted on Sunday, May 24th, 2009 at 2:49 am by Universe Queen

Problem 50:

The prime 41, can be written as the sum of six consecutive primes:
41 = 2 + 3 + 5 + 7 + 11 + 13

This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?

Answer: 997651

Implementation in Java:

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import java.util.Iterator;
import java.util.Set;
import java.util.TreeSet;
 
 
public class Euler50 
{
	public static boolean isPrime( int number )
	{
		if( number < 2 )
		{
			return false;
		}
		else if ( number == 2 )
		{
			return true;
		}
		else
		{
			for( long i=2; i<=Math.sqrt(number); i++ )
			{
				if( number%i == 0 )
				{
					return false;
				}
			}
		}
 
		return true;
	}
 
	public static void main(String[] args)
	{
		int result = 0;
		int maxLength = 0;
		Set primers = new TreeSet();
 
		for( int i=2; i<1000000; i++ )
		{
			if( isPrime(i) )
			{
				primers.add( i );
			}
		}
 
		Integer[] p = (Integer[])primers.toArray(new Integer[primers.size()]);
 
		for( int i=0; i<p.length; i++ )
		{
			long tmp = 0;
 
			for( int k=i; k<p.length; k++ )
			{
				tmp += p[k];
			}
 
			for( int j=p.length-1; j>i; j-- )
			{
				if( tmp < 1000000 && isPrime((int)tmp) && (j-i) >= maxLength )
				{
					maxLength = j - i;
					result = (int)tmp;
					break;
				}
 
				tmp -= p[j];
			}
		}
 
		System.out.println( result );
	}
}

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