Comments on search procedures for primitive roots

Eric Bach
1997 Mathematics of Computation  
Let p be an odd prime. Assuming the Extended Riemann Hypothesis, we show how to construct O((log p) 4 (log log p) −3 ) residues modulo 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.
doi:10.1090/s0025-5718-97-00890-9 fatcat:6xxziawpejdsvmr4aqsi4vqnxq