  Let $G$ be a finite primitive permutation group on a set $\Omega$ with
nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely
primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega
\setminus \{\alpha\}$. In earlier work, Mann, Praeger and Seress have proved
that every extremely primitive group is either almost simple or of affine type
and they have classified the affine groups up to the possibility of at most
finitely many exceptions. More recently, the almost simple extremely primitive
groups have been completely determined. If one assumes Wall's conjecture on the
number of maximal subgroups of almost simple groups, then the results of Mann
et al. show that it just remains to eliminate an explicit list of affine groups
in order to complete the classification of the extremely primitive groups. Mann
et al. have conjectured that none of these affine candidates are extremely
primitive and our main result confirms this conjecture.
