  We present a conjecture describing new long range correlations among the
Riemann zeros leading to 3 principal features: (i) The spectral
auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence
occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably
defined correlations lead to predictions (prophecy) of new zeros. This
conjecture is supported by analytical arguments and confirmed by numerical
calculations using 10^{22} zeros computed by Odlyzko. The results lead to a
self-duality of the Riemann spectrum similar to the quantum-classical duality
observed in billiards.
