A good prime is a prime with such that
for all integers with , where is the th prime (there is a typo in Guy 1994 in which the s are replaced by 1s). There are infinitely many good primes (Pomerance 1979, pp. 399-400). The first few are 5, 11, 17, 29, 37, 41, 53, ... (OEIS A028388).
More things to try:
Weisstein, Eric W. "Good Prime." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GoodPrime.html
with 
such that
with 
, where 
is the 
th prime (there is a typo in
Guy 1994 in which the 
s
are replaced by 1s). There are infinitely many good primes (Pomerance 1979, pp. 399-400).
The first few are 5, 11, 17, 29, 37, 41, 53, ... (OEIS A028388).
