That rules a lot of numbers out "early", but my code would still start checking them.

The estimate I made was

log_2 ( 10^85 ) < 283
log_3 ( 10^85 ) < 179
log_5 ( 10^85 ) < 121
log_7 (10^85 ) < 101

So, 9*84 * ( 283 * 179 * 101 + 179 * 121 * 101 ) = 5.5 billion

But the code avoids trying many of the possibilities 2^a 3^b 7^d, 0 < a < 283, 0 < b < 179, 0 < d < 101, because most of them are bigger than 10^85. Probably there's some smart way to get an estimate closer to 845 million by taking that into account.