  We test the spectrum of string theory on AdS_5 x S^5 derived in
hep-th/0305052 against that of single-trace gauge invariant operators in free
N=4 super Yang-Mills theory. Masses of string excitations at critical tension
are derived by extrapolating plane-wave frequencies at g_{YM}=0 down to finite
J. On the SYM side, we present a systematic description of the spectrum of
single-trace operators and its reduction to PSU(2,2|4) superconformal primaries
via a refined Eratostenes' supersieve. We perform the comparison of the
resulting SYM/string spectra of charges and multiplicities order by order in
the conformal dimension \Delta up to \Delta=10 and find perfect agreement.
Interestingly, the SYM/string massive spectrum exhibits a hidden symmetry
structure larger than expected, with bosonic subgroup SO(10,2) and thirty-two
supercharges.
