The importance of both the Boyle temperature (T-B) and temperature maximum (T-max) for the ability of intermolecular potential-based equations of state to accurately predict second virial coefficient (B) behavior was examined. The T-B, T-max, and B vs T behavior of several Lennard-Jones equations of state, developed from molecular simulation data, were compared with exact theoretical values. The analysis spanned low (T <= T-B), mid (T-B < T <= T-max), and high (T >> T-max) temperatures. The value of T-B was accurately predicted by most equations of state studied, whereas most failed to adequately predict T-max. The ability to accurately predict both T-B and T-max appears to be correlated with the accurate prediction of B values for the entire range of temperatures. This provides a useful criterion to improve future potential-based equations of state. The Mecke et al. and Thol et al. Lennard-Jones equations of state yielded the most accurate results. In some cases, a many-fold improvement in accuracy was observed compared with alternative equations of state. The exact B data were also used to obtain accurate polynomial relationships covering different ranges of temperatures.