Can prime numbers be generated by a formula? I think this question comes to the mind of everyone who starts learning about prime numbers. 
In particular one might ask this question:
is there any dynamical system that walks through the prime numbers? in other words is there any way to calculate P_N (the Nth prime)
from the set  {P_1,P_2,...,P_N-1}?
To the best of my knowledge,  there is no known answer for this question.  When I first read Euclid's proof for prime numbers
(about 15 years ago), a conjecture came to my mind which, if true, gives a way to build up such a machine for generating primes.
I haven't been able to prove or disprove it yet and I really appreciate it if you can do that for me :)