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>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 won't even ask. I'll just chalk it up to "My tax dollars at work".:-)

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>>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

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

It may especially in the run time environment (and with those numbers).