>But, let me answer question. I don't deal with the same type of data or same situations that you do. However, in those cases where a large numer of iterations are required, I've had success in re-examining the problem to see if there is a smaller subset that can be used.

2**20 _IS_ a smaller subset, it was 2**40 before invoking some theory :) But your point is on target, this current work is an math optimization problem. 2**20 is small potatoes in this league, in order to get publishable results I'm likely going up to 2**1000 or so, no small run-time (I think we're talking years here)...it will not be solvable without some major theoretical optimization, I think...

>I certainly don't mean to pick, my friend, but your example brings a question to mind. If speed is so essential there, why do you force the system to re-evaluate the terminating expression (2**20 or 2^20) every time through the loop. You gain more speed by:

>lnlast = 2 ^ 20
>FOR ncount = 1 TO lnlast
>  * The same stuff here
>ENDFOR

Hey, nice tip...hadn't even occurred to me. That could add up to big savings...