Brian Beesley wrote: > On Sunday 01 October 2006 07:16, Nacho wrote: > >> Hello everyone. >> >> I'm a little surprised that nobody said it, but such function is known. >> It is called Pi(x), and gives the number of primes less than x. The main >> problem is the implementation of Pi(x), of course. >> > > Doesn't this depend on the (AFAIK unproved) Riemann hypothesis? > Not certain of this, but I think Pi(x) is defined as the number of primes less than or equal to x. The Riemann hypothesis is concerned with a particular approximation to Pi(x), a more accurate one than Pi(x) = x / lg x. >> Maybe the algorithm developed by Allen is new, but there are some other >> algorithms used. >> > > This is where the possible interest is. If Allen's algorithm turns out to be > genuinely different, proveably correct and returns the same results as Pi(x) > then there may be a handle on proving Riemann. Or even the extended Riemann > hypothesis! > > Regards > Brian Beesley > Hmm, unlikely. Allen's algorithm sounds like it's at least as computationally intensive as finding the primes individually.
Soo Reams _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
