OFFSET
1,1
COMMENTS
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]
FORMULA
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)]]
MATHEMATICA
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]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, May 24 2004
STATUS
approved