A very naive Java program finding the smallest Lychrel number

LychrelLibrary.java

public class LychrelLibrary {
	public static String reverseString(String string) {
		return new StringBuffer(string).reverse().toString();
	}

	public static long reverseNumber(long n) {
		return Long.valueOf(reverseString(String.valueOf(n)));
	}

	/**
	 * This is in a way a halting problem. Our best estimation
	 * is checking for each number for as long as we can, and
	 * if we overflow long then we assume it's a Lychrel number
	 * (although it might not be!)
	 * 
	 * @return a smallest number we think might be a Lychrel
	 */
	public static long findSmallestLychrel() {
		long candidate = 0;
		while (true) {
			if (mightBeALychrelNumber(candidate))
				return candidate;

			candidate++;
		}
	}

	public static boolean mightBeALychrelNumber(long number) {
		// If the long overfloats we have no chance of finding
		// the palindrome, so it is an indication that
		// the number might be a Lychrel number
		while (number >= 0) {
			number += reverseNumber(number);
			if (isPalindrome(number))
				return false;
		}

		return true;
	}

	public static boolean isPalindrome(long number) {
		String numberAsString = String.valueOf(number);
		return numberAsString.equals(reverseString(numberAsString));
	}

	public static void main(String[] args) {
		System.out.println(findSmallestLychrel());
	}
}