  In this paper we study the (classical) Frobenius problem, namely the problem
of finding the largest integer that cannot be represented as a nonnegative
integral combination of given relatively prime (strictly) positive integers
(known as the Frobenius number). The main contribution of this paper are
observations regarding a previously known upper bound on the Frobenius number
where, in particular, we observe that a previously presented argument features
a subtle error, which alters the value of the upper bound. Despite this, we
demonstrate that the subtle error does not impact upon on the validity of the
upper bound, although it does impact on the upper bounds tightness. Notably, we
formally state the corrected result and additionally compare the relative
tightness of the corrected upper bound with the original. In particular, we
show that the updated bound is tighter in all but only a relatively "small"
number of cases using both formal techniques and via Monte Carlo simulation
techniques.
