  We introduce a notion of characteristic for connective $p$-local $E_\infty$
ring spectra and study some basic properties. Apart from examples already
pointed out by Markus Szymik, we investigate some examples built from Hopf
invariant $1$ elements in the stable homotopy groups of spheres and make some
conjectures about spectra for which they may be characteristics; these appear
to involve hard questions in stable homotopy theory.
