And you can't go further, so there is no n for that n^k+n+1 is semiprime for k=1,2,3,4,5. Proof: v=n^5+n+1=(n^2+n+1)*(n^3-n^2+1), here n^2+n+1 is semiprime, so for n>1 v=n^5+n+1 has got at least 3 factors (so bigomega(v)>2), hence not a semiprime.