Eli Brandt writes:

...

Victor S. Miller, [who I suspect is the same Victor S. Miller I knew at UMass Boston many years ago], published a nifty little paper in the mid 1980's on the computation of the function Pi(n)

Do you have a pointer to this paper? I'd been under the impression that this function had no analytic closed form (unless you cheat).

I'll also post this to the list since I need to correct a dumb error in my previous post. I previously stated that Pi(n) was the Nth prime. It is of course in reality the Prime Number Counting Function which is equal to the number of primes <= n. Computing the Nth prime is trivial given a program which computes Pi(n) since Pi(n) is asymptotic to a known smooth function and one need only evaluate it a small number of times to refine an initial estimate of the Nth prime into the correct value. Miller's definitive paper on the subject is... Computing Pi(x): The Meissel-Lehmer method Mathematics of Computation, 1985, 44, no. 170, 537-560 There is another paper by this gentleman which may be of interest to Cypherpunks. It is on the use of elliptic curves as a basis for cryptosystems. He demonstrates how an analogue to the Diffie-Hellman secure key exchange may be constructed using groups of points on elliptic curves and conjectures that such a system may be stronger than one based on the discrete log problem. Here is the citation. Use of elliptic curves in cryptography Advances in cryptology---CRYPTO 85 1986, 417-426 ISBN: 0-387-16463-4 Happy reading. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd@netcom.com $ via Finger. $