Find the longest(?) string of consecutive frugal numbers.

Def: A frugal number is a natural number that has more digits than the number of digits in its prime factorization (including exponents). For example, 128=2^7 and 29282=2*11^4

The longest one I could think of from the top of my head was from 1034429177995381247 to 1034429177995381255, which is 9 digits long. There is actually no "longest" string of consecutive frugal numbers however, as you can always find a longer string of frugal numbers. (I did however assume that the Dickson conjecture holds)