The Lychrel numbers are the number for which the following algorithm, known as the 196 algorithm, is not known to terminate:

On each step, if our number is not palindromic, reverse its digits and add the result to itself. Terminate if the number is palindromic.

For example, we start with the number 152, the first step tells us to reverse the digits, obtaining 251, and then add this result to the original number, giving us 403. On the next step, we do the same thing, obtaining 403 + 304 = 707. This is a palindromic number, so the algorithm stops.

When applied to 196, this algorithm never appears to stop, but there is no proof that it won't stop eventually at some very large number. This market resolves YES if it is proven that the algorithm never terminates when we start with 196, and NO if it is shown to terminate.