That's very clever but you do appear to have chosen bounds that trivialise the problem. Try largest(1000, 1001, 1003)
100,000 isn't large enough, try 1,000,000 and then go make a cup of tea (actually you could probably grow a cup of tea in the time this will take)
Update Hmm.... the original did say not to worry about efficiency but it's not hard to produce examples with fairly small numbers that will run for years, maybe even centuries.
I've been waiting more than 7 minutes just to find out if 999999 is possible with largest(1000, 1001, 1002, 1003, 1004, 1005) and there's no sign of an answer yet.
Update again I killed it after 100 min of CPU time (1.7Ghz Pentium) and it still hadn't figured out if 999,999 was doable or not.