Exhaustive prime search: we check every single candidate.

ExhaustivePrimeSearch.java

import java.math.BigInteger;

/** Tests for a prime by checking every single candidate. */
public class ExhaustivePrimeSearch extends PrimalityTest {
    @Override
    public boolean isPrime(BigInteger n) {
        // Only need to check numbers from 2 up to the square root.
        BigInteger candidate = BigInteger.valueOf(2);
        
        while ( (candidate.pow(2)).compareTo(n) == -1 ) {
            if ( n.mod(candidate).compareTo(BigInteger.ZERO) == 0) {
                // We have found a divisor here, so we don't have a prime.
                return false;
            }
            
            candidate = candidate.add(BigInteger.ONE);
        }
        
        // If we got here, then no divisor was found; n is definitely prime.
        return true;
    }    
    
    public static void main(String[] args) {
        (new ExhaustivePrimeSearch()).timedPrimeTest(
                new BigInteger(args[0]) );
    }
}