  Let $p$ denote a prime number. In this note, we focus on the modular
Terwilliger algebras of association schemes defined in [3]. We define the
primary module of a modular Terwilliger algebra of an association scheme and
determine all its composition factors up to isomorphism. We then characterize
the $p'$-valenced association schemes by some properties of their modular
Terwilliger algebras. The corollaries about the modular Terwilliger algebras of
association schemes are given.
