> Huh! Would you believe that? The 64^15 is so big compared to the others that the difference is only in the second decimal place in bits. > > For some people, the actual number would be more intuitive (not me, but maybe you): Perhaps even more intuitive to others would be to look at the available characters like an all-inclusive dictionary (I'll just use a small a-z example to keep it simple): aaaa .... zzzz and realize that each additional letter creates *multiples* of the smaller dictionary: aaaaa a.... azzzz baaaa b.... bzzzz ..... zzzzz Or, put another way, getting back to the math, the number of combinations you gain by including the lesser length combinations is no greater than you get from a single subset of the next higher length, so for your example: l(64^16 / 63)/l(2) 90.02272007650008353057 > So adding all the other lengths only added about 1.5% to the number of combinations! To be exact, it can only add the corresponding fraction of your chosen alphabet size, in this case: 1/64 .01562500000000000000 aef3225562b46c4e9bb4cf0987e8253e0e535f607c2affbc4466e1ac979ac0c4