Primality proving for 'near-powers'

[CRGreathouse]

Is there a method for proving the primality of large numbers of the form
$$a^b+c$$
where a and c are of similar size? I'm looking for something faster than a general primality prover like PRIMO, or a comment like "I know of no such method".

 

[Hurkyl]

That's exactly what the special number field sieve was designed to do.

 

[CRGreathouse]

I'm looking to prove primality, not factor. I'm looking for an analogue of SNFS for primality.

 

[Hurkyl]

Good point. Sorry 'bout that.

 

[CRGreathouse]

Good point. Sorry 'bout that.

Frankly, I did *exactly* the same thing myself: I said "that's a perfect SNFS form!" and Googled to find a good client... until I realized that I was searching for the wrong thing.

Can you verify that you know of no algorithm/program/whatever to do this quickly? That way, if I resort to some standard method like ECPP, I won't feel like I'm doing it an unreasonably hard way.