  We report on calculations of Feynman periods of primitive log-divergent
$\phi^4$ graphs up to eleven loops. The structure of $\phi^4$ periods is
described by a series of conjectures. In particular, we discuss the possibility
that $\phi^4$ periods are a comodule under the Galois coaction. Finally, we
compare the results with the periods of primitive log-divergent non-$\phi^4$
graphs up to eight loops and find remarkable differences to $\phi^4$ periods.
Explicit results for all periods we could compute are provided in ancillary
files.
