Let
p
p
be an odd prime. Assuming the Extended Riemann Hypothesis, we show how to construct
O
(
(
log
p
)
4
(
log
log
p
)
−
3
)
O( {(\log p)^{4} (\log \log p)^{-3} } )
residues modulo
p
p
, one of which must be a primitive root, in deterministic polynomial time. Granting some well-known character sum bounds, the proof is elementary, leading to an explicit algorithm.