  This note presents an upper bound for the least prime primitive roots
$g^*(p)$ modulo $p$, a large prime. The current literature has several
estimates of the least prime primitive root $g^*(p)$ modulo a prime $p\geq 2$
such as $g^*(p)\ll p^c, c>2.8$. The estimate provided within seems to sharpen
this estimate to the smaller estimate $g^*(p)\ll p^{5/\log \log p}$ uniformly
for all large primes $p\geq 2$.
