True beyond reasonable doubt

Number Theory has some of the flavour of an experimental science. Numerical calculations may be used to gather evidence in favour of (or against) conjectures, and may in fact lead to the formulation of new conjectures. Computers provide the mathematician with an efficient tool for gathering this evidence. But you have to be careful. Mathematics does not take too kindly to being treated in an offhand manner, and has quite a few surprises in store for the unsuspecting computer user. Or for the unsuspecting mathematical genius for that matter. Even the great Fermat fell into the trap of extrapolating from numerical evidence to what turned out to be a false conclusion. In honour of his mistake, numbers of the form