Primus-Orderus Primes
Mathematica, 104 bytes

Extremely efficient

(t=i=1;While[t&lt;#+1,If[!FreeQ[Subsets[(r=IntegerDigits)@Prime@i,{Length@r@i}],r@i],t++];i++];Prime[i-1])&amp;



finds n=34 in under a minute