Why have Majorana fermions not been detected? There are two types of fermions - Dirac's and Majorana's. Majorana's fermions are their own antiparticles and they have not been detected yet. Sometimes, it is conjectured that e.g. neutrinos could be Majorana fermions.
However, it seems to me that there should be no Majorana fermion in current Universe. When particle and its antiparticle meet, they anihilate each other. Since there is no distinction between particles and antiparticle in case of Majorana fermions, a bunch of Majorana fermions should completely anihilate (maybe one particle can surive in case there were odd number of the particles in the bunch). This should happen shortly after Big Bang when all type of particle were created and the Universe was still small. Perhaps we could create Majorana fermions in accelerators, however, I suppose we should not be able to detect them in the Nature.
Does my reasoning make sense? If not, what am I missing?
 A: 
Since there is no distinction between particles and antiparticle in case of Majorana fermions, a bunch of Majorana fermions should completely annihilate

It is not that simple, to model a baryon dominated universe. The same thoughts for Dirac fermions lead to the problem of why there is baryon asymmetry in the observed universe.

According to the Big Bang theory, equal amounts of matter and anti-matter were initially created. When matter and anti-matter come into contact, they annihilate into pure energy, producing photons and nothing else. The relic of this primordial annihilation is the Cosmic Microwave Background, the 2.7 Kelvin radiation that fills the entire Universe. But not all of the matter annihilated into photons: about one out of every billion quarks survived and originated the Universe as we know it today. How could some matter survive the primordial annihilation?

So it is not a matter just for Majorana neutrinos. If you read the link you will see that the question of their existence is still open to research.
A: Dirac equation is not all we have - there are also "boundary conditions" or some experimental input. Only that together determines uniquely the solutions. No Majorana input data, no Majorana solutions in practice.
