Fast prime finder??

[ttw]

For exponentiation of large numbers, a reasonable (if not optimal) strategy is to use binary exponentiation followed by a modular reduction at each step. Intermediates can be held to no more that twice the number of digits as the numbers of interest. Optimal orders of multiplication (factorization of the exponent or a tree structure, see Knuth vol. 2) are only useful if the same exponent is used repeatedly.