HumbleGenerator[max_] :=
 Sort[Flatten@ParallelTable[
    2^i 3^j 5^k 7^m, {i, 0, Log[2, max]}, {j, 0, Log[3, max/2^i]}, {k,
      0, Log[5, max/(2^i 3^j)]}, {m, 0, Log[7, max/(2^i 3^j 5^k)]}]]

{"First 50 Humble Numbers:",
  HumbleGenerator[120],
  "\nDigits\[Rule]Count",
  Rule @@@ Tally[IntegerLength /@ Drop[HumbleGenerator[10^100], -1]] //
    Column} // Column