"Costello, Roger L."
Thank you for your detailed explanation. I am not sure that I understand all of its subtleties.
I am wondering if you would be willing to provide us with a simple, complete example that we can try out on our own machines?
I have written the Lucas-Lehmer primality test in various variants in the this paste: http://hpaste.org/86449 The gist of it is that for a prime p you generate a sequence, pick a particular element from it and compare it to zero. If it is zero, then 2^p - 1 is a prime number. In the paste the llSeq function is universal to both the pure algorithm (llTest) that only computes the result as well as the stats variant (llTestStats) that is an IO action and tells you how many iterations are left to go. For comparison I have also written a monolithic variant (llTestMono) that doesn't use the stream processing style and shows how you would implement the same algorithm in an imperative language. This is monolithic in that there is no flexibility here. They are all about equal in speed. Just compile and run with the argument 10007: ./lucas-lehmer 10007 This will test whether the number 2^10007 - 1 is prime. It should be finished in less than a second and conclude with False. The argument 11213 will conclude with True. Greets, Ertugrul -- Not to be or to be and (not to be or to be and (not to be or to be and (not to be or to be and ... that is the list monad.