What can be gleaned about primes from Algebraic Number Theory? I know this is too vague. What I mean is the following: 

**Are there several examples where Algebraic Number Theory helps to solve ancient/long-standing problems about primes?**

Instances such as representibility of primes by quadratic forms [1][1] and the quadratic reciprocity law [2][2] have been suggested. **What role does ANT play in the theory of prime numbers, specifically prime distribution, gaps and progressions?** (Are there corresponding algebraic studies of these questions (in contract to the analytic point of view)?  

I would be grateful if you point me to a survey on such topics. It doesn't hurt if the answer is No/None/Nothing, etc.
Thanks.


  [1]: http://en.wikipedia.org/wiki/Kaplanskys_theorem_on_quadratic_forms
  [2]: http://en.wikipedia.org/wiki/Quadratic_reciprocity