Using this we can actually predict the smallest exponent that fails for other bases:

  base	exponent (6 digits)
  10	0.043429
  11	0.041703
  12	0.040243
  2	0.144271
  3	0.091024
  4	0.072135
  1000	0.014476

(the calculated exponent for two is actually 0.144270, but since it ends in zero the first failure occurs at 0.144271)