There is an algorithm, that given a number k, and n, generates all numbers such that n of them add up to k. IE for k = 10, n = 3:
bonus if you can do it in terms of expt modulo
1,1,7 1,2,8 1,3,6 1,4,5 1,5,4 (i guess barring permutations) etc…
What this will do is completely eliminate any efficiency in terms of ” oh this isn’t even odd! ”
Unfortunately, the reason this project is abandoned right now is that this solution still won’t solve the fundamental problem: We need a linear time algorithm to get anywhere near 10^14.