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%I #6 Mar 30 2012 17:34:14
%S 2,3,5,13,43,53,61,79,83,127,131,139,157,223,251,313,337,347,367,397,
%T 463,479,499,541,547,557,643,659,769,797,853,859,887,991,1031,1049,
%U 1201,1213,1231,1237,1249,1279,1291,1297,1303,1321,1327,1381,1399,1583,1601
%N An asymptotic prime formula derived from a vibrational Hilbert space model for the zeta zeros.
%C This formula was derived in Mathematica in a Laplacian Hilbert space model using zeta zero like functions to give a spectrum. This specific approach to the Riemann conjecture was suggested by Hilbert himself. Equations for the model are: Phi[n_,s_]=Exp[ -s^2/(4*n)]/n^(s/2)+I*(Exp[ -s^2/(4*n)]/n^(s/2)) H*Phi = \(d\_\(s, s\)\[Phi] + V\[Phi] = E0[n] \[Phi]\)\ \)\) E0[n_]=hbar*(1/2+I*b[n]) Solve[V==0,b[n]] Solve[Im[b[n]]==0,s]
%F If Floor[Abs[n*log(n)-Sqrt(n*(n+2*Pi)/Pi)]] is prime then Floor[Abs[n*log(n)-Sqrt(n*(n+2*Pi)/Pi)]]
%t s=-n*log(n)+Sqrt[n*(n+2*Pi)/Pi)] a=Delete[Union[Table[If[PrimeQ[Floor[ -s]]==True, Abs[Floor[ -s]], 0], {n, 1, 500}]], 1]
%K nonn,uned
%O 1,1
%A _Roger L. Bagula_, May 24 2004
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