I want to find the first 5 prime numbers of the form $n^6 + 1091$. I have used this code:

 Timing[Select[Table[n^6 + 1091, {n, 10000}], PrimeQ, 5]]

Which gives the desired answer, and takes 0.0156 seconds. What if I didn't have a rough idea of what values of $n$ to check? 

 Timing[Select[Table[n^6 + 1091, {n, 100000}], PrimeQ, 5]]

Takes 10 times as long.
 
So, my question is: Is there a simple(ish) way to make *Mathematica* stop when the desired number of solutions are found?