Tom Womack on Thu, 25 May 2000 17:22:57 +0100 |
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This *can't* be missing, can it? |
What are the pari names for pi(x) [the inverse function for prime(x)] and pimax [the largest value for which prime(x) is a precomputed prime]? It's trivial to write a little binary-search routine { pith(x) = local(t,l,r); t=1; while(prime(t)<=x,t=t*2); l=t/2;r=t; while (r-l>1,m=(l+r)/2;if (prime(m)<=x,l=m,r=m)); l; } but that works badly if X is near enough to primelimit for the first while loop to overshoot, and feels as if it ought to be a primitive function in any case. I'm trying to implement the Buhler-Gross clever algorithm for computing L^(r)(1) (which requires only sqrt(n) storage to do a sum up to a_n, and so should converge reasonably for conductors up to O(available storage ^ 4) ), with the eventual aim of adding an ellanalyticrank(e) function to Pari [would this be useful functionality?]; this is just the first step to know how many primes I need to store. Tom