My ACT conjecture
> We should try to collect as many of very hard to prove or disproveHans, here's my ACT conjecture, of you like :
> conjectures about primes as ever possible of any of the types ACF
> or ACT to convince Chris Caldwell that such an ACF/ACT conjectures
> page would be a page of it's own right among his prime pages.
> Which ACF/ACT conjectures about (or including) primes are
> known to you?
For fixed, relatively prime naturals a,b, every large enough number
of the form ax+b is the average of two primes of the form ax+b.
This, apparently, is a GC-like conjecture for the infintely many
primes on the series ax+b. Goldbach's conjecture is actually a
special case of the above conjecture as the set of naturals, in which
GC is defined, is a special case of ax+b, with a=1.