Examples

One can show that if an integer of the form 2**k+1 is prime, then k must be a power of two. Pierre Fermat conjectured that every integer of the form 2**(2**n)+1 is prime. Let's look for a counterexample. First define a function:

Now try commands like:

until you find an integer of this form which is composite. You can also try the following command:

Obviously, Fermat didn't have access to Axiom.