f(p) = 0 tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 06/05/2011, 04:46 PM (This post was last modified: 06/07/2011, 11:52 AM by tommy1729.) since this does not relate to tetration , ill post it here. it is easy to construct functions f(x) such that f(x) is analytic for REAL x > 1 and f(p) = 0 IFF p is a prime. something looking similar to sin(pi x)^2 + sin( gamma(x)/x pi )^2 for instance. however , it seems harder to find an entire function f(z) that satisfies f(z) = 0 IFF COMPLEX z = prime. i heard about zeta functions and L-series , but i was thinking about simpler solutions. Moderators note: Community Subforum is not for discussion of mathematical topics. tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 06/13/2011, 07:05 AM (This post was last modified: 06/13/2011, 08:57 AM by bo198214.) $\sin(\pi x)^2 + \sin( (\Gamma(x+1) (1 - ((x/2) (\Psi(x/2 + 1/2) - \Psi(x/2)) - 1/2) \sin(\pi x) / (\pi x)))/(x+1) \pi )^2$ is nicer ; it satisfies f(p) = 0 and is entire. but i dont know where are the other zero's ... regards tommy1729 Mod note: If you use tex why not use it to make it more readable? I modified your formula accordingly. « Next Oldest | Next Newest »