Primes p such that x = order(x) modulo p

[Nick Hobson]

Hi seqfans,

The following primes are such that for at least one x in 2...p-1, the  
order of x modulo p is equal to x.  For example, the order of 3 modulo 13  
is 3, since 3^3 = 1 (mod 13), while 3^2 and 3^1 != 1 (mod 13).

3, 11, 13, 17, 19, 29, 31, 37, 41, 53, 59, 61, 67, 71, 73, 83, 89, 97

PARI script: forprime(p=3, 97, for(x=2, p-1, if(znorder(Mod(x, p))==x,  
print1(p, ", "); break)))

Is this of general interest?

What about primes for which order(x) = y and order(y) = x, for at least  
one pair (x,y), not necessarily distinct?  (Such primes form a superset of  
primes for which 2 is a primitive root modulo p.)

Nick