The description of the problem itself explains a way to verify that intermediate results are correct.
> Did you have an estimation of the date?
Yes and that one is easy: I wrote a little piece of code (in Clojure, whatever, it's unrelated to finding the solution) which would check at which intermediate result the computation was and then compute an "ETA".
Fun story: I'd regularly send my brother something like this...
:eta "1 year 2 month(s) 26 day(s)"
(that's an actual estimate I found in my old emails)