It can provide false positives but not false negatives, so it's good enough because the goal was only to prove that the number on the pencil is the largest left

It can provide false positives but not false negatives, so it's good enough because the goal was only to prove that the number on the pencil is the largest left-truncatable prime. If it provided a positive result the author would have checked that one separately or added more primes to the check.