Approximating Primes

A successful strategy to handle problems involving primes is to approximate them by a more 'simple' function. Two aspects need to be balanced. On the one hand, the approximant should be simple enough so that the considered problem can be solved for it. On the other hand, it needs to be close enough to the primes in order to make it an admissible to replacement. In this talk I will present how one can construct general approximants in the context of the Circle Method and will use this to give a different perspective on Goldbach type applications.