nt.number theory - Infinitely many prime numbers of the form $n^{2^k}+1$?

It took me a while to find this: http://www.pnas.org/content/94/4/1054.full

Anyway by Friedlander and Iwaniec (1997). They proved that there are infinitely many primes of the form $x^2 + y^4 .$ They mention near the end that they do not have a proof for primes of the form $x^2 + y^6 $ but would like one. So there is a way to go to settle $x^2 + 1.$

FYI, what I did (not remembering title, authors, anything but the result) was write a program to give the primes $x^2 + y^4 $ and put the first dozen in Sloane's sequence site search feature.