Just to explore those incomplete sets of permutations of digits:
cand = With[{l = PrimePi[100],
u = PrimePi[10000]},
GatherBy[Prime /@ Range[l + 1, u - 1], Sort[IntegerDigits@#] &]];
fun[n_] := Multinomial @@ Tally[IntegerDigits@n][[All, 2]]
res = SortBy[Select[cand, Length@# > 1 &], Length];
all = GatherBy[
If[fun[#[[1]]] == Length@#, Style[#, Red, Bold] & /@ #, #] & /@
res, Length];
Column@With[{s = Ceiling[Sqrt@#] & /@ Length /@ all},
MapThread[
Length[#1[[1]]] ->
Grid[Partition[PadRight[#1, #2^2, ""], #2],
Frame -> True] &, {all, s}]]
