/**
 * Test harness for an implementation of the Luhn algorithm that checks the
 * validity of a credit card number.
 */
public class Luhn {
	/**
	 * Main entry point for the test harness.
	 *
	 * @param args the command line arguments.
	 */
	public static void main(String[] args) {
		if (args.length < 1) {
			System.err.println("Usage: Luhn number ...");
			System.exit(1);
		}

		for (int i = 0; i < args.length; i++) {
			System.out.print("Number '" + args[i] + "'" );
			if (!args[i].matches("^\\d{13,19}$")) {
				System.out.println(" is not a valid credit card number (must be 13-19 digits)");
			} else if (isValidNumber(args[i])) {
				System.out.println(" is a valid credit card number");
			} else {
				System.out.println(" is not a valid credit card number");
			}
		}
	}

	/**
	 * Checks whether a string of digits is a valid credit card number according
	 * to the Luhn algorithm.
	 *
	 * 1. Starting with the second to last digit and moving left, double the
	 *    value of all the alternating digits. For any digits that thus become
	 *    10 or more, add their digits together. For example, 1111 becomes 2121,
	 *    while 8763 becomes 7733 (from (1+6)7(1+2)3).
	 *
	 * 2. Add all these digits together. For example, 1111 becomes 2121, then
	 *    2+1+2+1 is 6; while 8763 becomes 7733, then 7+7+3+3 is 20.
	 *
	 * 3. If the total ends in 0 (put another way, if the total modulus 10 is
	 *    0), then the number is valid according to the Luhn formula, else it is
	 *    not valid. So, 1111 is not valid (as shown above, it comes out to 6),
	 *    while 8763 is valid (as shown above, it comes out to 20).
	 *
	 * @param number the credit card number to validate.
	 * @return true if the number is valid, false otherwise.
	 */
	private static boolean isValidNumber(String number) {
		int sum = 0;

		boolean alternate = false;
		for (int i = number.length() - 1; i >= 0; i--) {
			int n = Integer.parseInt(number.substring(i, i + 1));
			if (alternate) {
				n *= 2;
				if (n > 9) {
					n = (n % 10) + 1;
				}
			}
			sum += n;
			alternate = !alternate;
		}

		return (sum % 10 == 0);
	}
}

http://www.chriswareham.demon.co.uk/software/Luhn.java

Test harness for an implementation of the Luhn algorithm that checks the validity of a credit card number.

Luhn Formula (Algorithm)

class, validation

Java