Implementation of Fermat's primality test

Question

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I\'m try to implement Fermat\'s primality test in Java using BigIntegers. My implementation is as follows, but unfortunately i

Answer 1

Your use of the particular BigInteger constructor is reasonable, but you should use a rejection method to select a fermat base a. Here is a slight modification of your method in a class which also uses exactly one Random object:

import java.math.BigInteger;
import java.util.Random;

public class FermatTestExample
{

    private final static Random rand = new Random();

    private static BigInteger getRandomFermatBase(BigInteger n)
    {
        // Rejection method: ask for a random integer but reject it if it isn't
        // in the acceptable set.

        while (true)
        {
            final BigInteger a = new BigInteger (n.bitLength(), rand);
            // must have 1 <= a < n
            if (BigInteger.ONE.compareTo(a) <= 0 && a.compareTo(n) < 0)
            {
                return a;
            }
        }
    }

    public static boolean checkPrime(BigInteger n, int maxIterations)
    {
        if (n.equals(BigInteger.ONE))
            return false;

        for (int i = 0; i < maxIterations; i++)
        {
            BigInteger a = getRandomFermatBase(n);
            a = a.modPow(n.subtract(BigInteger.ONE), n);

            if (!a.equals(BigInteger.ONE))
                return false;
        }

        return true;
    }

    public static void main(String[] args)
    {
        System.out.printf("checkprime(2) is %b%n", checkPrime(BigInteger.valueOf(2L), 20));
        System.out.printf("checkprime(5) is %b%n", checkPrime(BigInteger.valueOf(5L), 20));
        System.out.printf("checkprime(7) is %b%n", checkPrime(BigInteger.valueOf(7L), 20));
        System.out.printf("checkprime(9) is %b%n", checkPrime(BigInteger.valueOf(9L), 20));
    }
}

Answer 2

a should be "pick a randomly in the range (1, n − 1]" and I don't really see that happening. You could print a to check that.

As for how to do that:

BigInteger a = BigInteger.valueOf(random.nextInt(n-2)+2);

e.g. You shouldn't use the BigInteger constructor with a Random argument; that's just a source of randomness, but a should be a random value.

The 'random.nextInt(n-1)+1' comes from the definition of nextInt which, given argument k, returns a random value 0 up to and including k-1. And you want a to be larger than 1 and smaller than n.