While completelely factorizing integers, my student Luciana noticed that the canonical prime factorization of the three consecutive numbers 81=3^4, 82=2x41, and 83=83, use numbers which are all different: 2,3,4,41, and 83. She would like to know the largest possible triplet of such numbers. I told her it was likely that such triplets occur infinitely often, but a matter difficult to prove.
"What then is the largest such triplet you can find?",-she asked. I told her I would pass the question to someone abler than me.