  We study the complexity of $\mathscr{B}$-free subshifts which are proximal
and of zero entropy. Such subshifts are generated by Behrend sets. The
complexity is shown to achieve any subexponential growth and is estimated for
some classical subshifts (prime and semiprime subshifts). We also show that
$\mathscr{B}$-admissible subshifts are transitive only for coprime sets
$\mathscr{B}$ which allows one to characterize dynamically the subshifts
generated by the Erd\"os sets.
