One runs a computer program and notices this is true up to very large integers n (greater than two), and positive integers a, b, and c up to very large numbers which the computer can handle.
Would this be anecdote or evidence, in support of Fermat's Last Theorem?
Who is the "one"?
I run a computer program and notice that this is true is evidence (to me) and anecdote (to you). After all, you have only my statement that it is so, and, like your poker-playing buddies with the "magic touch", my statement is subject to question.
This is, AFAICT and in accordance with my education, an important part of the scientific method. You do not have to trust my word; you can repeat the experiment yourself. You can build up your own experiences through conducting the experiment yourself. If your experiences contradict mine, you should not take mine as evidence.
At some point, of course, the number of experiments you'd have to do to gain evidence becomes too great, and requires too great an expense. That is why the scientific community uses peer review and independent confirmation of experiments. The value of these is no less, and no more, than the value one places on the truthfulness, diligence, and intelligence/understanding of those involved.
Testimony is only evidence (to you) if it passes your personal barrier of skepticism.
The less a claim conforms to your expectations (based on your experience and your interpretation of experience), the greater the barrier of skepticism. For most people, anyway.
RC