  For any given number of crossings $c$, there exists a formula to determine
the number of 2-bridge knots of $c$ crossings, and indeed it is a simple matter
to actually construct presentations of these knots. However, the determination
of whether a given (prime) knot is a 2-bridge knot remains a nontrivial
exercise, and we have no procedure to determine bridge numbers more generally.
Herein, we identify the 2-bridge knots within the Hoste--Thistlethwaite--Weeks
tables of prime knots of up to 16 crossings by an exhaustive search of a larger
set of 2-bridge knots. As the unknot is the only knot with bridge number 1,
this yields a lower bound of 3 for the bridge numbers of the remaining knots.

Geometric Topology