Prime power conjecture

Tommy's prime power conjecture 

Let p be a prime such that p−2 is also a prime.

Then there is always an integer n>1 such that 

q_n = p^n−2

and 

q_n is also a prime.

This is a special case of the generalized Bunyakovsky conjecture. 

See also

https://oeis.org/A267944

and 

https://math.stackexchange.com/questions/4841269/primes-of-the-form-q-n-pn-2

It is probably true for Eisenstein primes too.

https://en.wikipedia.org/wiki/Eisenstein_integer#Eisenstein_primes

picture : the Eisenstein primes.