What size laminated timber beam is needed for a 23 foot clear span under a 15 foot roof in between load bearing walls?

38 feet long

It is not possible to give a definite answer without more detail. The construction and type of roof will determine the load (weight) bearing on the beam, and factors such as wind load and earthquake load, and the way the roof bears on the beam (truss/point load/distributed load) will all affect the sizing.