The very requirement for antiparticle is not that they annihilate.
Antiparticles is just the opposite charge and spin (time reversed particle), and SOME antiparticles will annihilate if they interact with each other. Now in standard QED, photon-photon interactions is not possible (at least not with a virtual photon coupling, but with several virtual electron/positrons)
see http://universe-review.ca/R15-12-QFT.htm
So in one sense two photons will annihilate and form photons again ;-)
I mean, what is meant by annihilation in physics anyway?
The antiparticle of the neutron is the antineutron, which has the constituent anti-quarks of the neutron, eg. 2 anti-down, 1 anti-up
Since E = mc^2, how can photons be massless? If a photon has no mass, then, according to Einstein's formula, its energy is given by E = 0 x c^2, which is 0. Yet, photons do have energy. This seems to be a complete contradiction. Please explain! Thank you.