Sure, P(I'm mistaken about whether 53 is prime) is non-negligible (I've had far worse brain farts myself).

But P(I'm mistaken about whether 53 is prime|I'm not sleep-deprived, I haven't answered a dozen similar questions in the last five minutes, and I've spent more than ten seconds thinking about this) is several orders of magnitude smaller.

And P(I'm mistaken about whether 53 is prime|[the above], and I'm looking at a printed list of prime numbers and at the output of factor 53) is almost at the blue tentacle level.