Greetings from EuroCG 2012, from which I post via iPod, so apologies for lack of problem motivation, background research and mathematical formatting.
Question:Suppose L is a horizontal or vertical line in the argand plane passing through a Gaussian prime. Are there infinitely many Gaussian primes on L?
In fact, all I need is a next prime along a line, but of course if that was guaranteed one could repeat the process to keep going forever. Still, if there is a next prime, some idea of how far along it is might also be useful for the application in mind.
Hopefully equivalent question for rational primes in rational integer sequences: let s(k)=a^2+(b+k)^2$s(k)=a^2+(b+k)^2$ for k>=0$k\ge0$. if s(0)If $s(0)$ is prime, does the sequence {s(k)}$\{s(k)\}$ contain infinitely many primes?