FastECPP is currently the fastest approach to prove the primality of general numbers, and has the additional benefit of creating certificates that can be checked independently and with a lower complexity. It crucially relies on the explicit construction of elliptic curves with complex multiplication. I will take you on a leisurely stroll through the different phases of the ECPP and fastECPP algorithms, with explanations of their complexity. We will then see the algorithmic choices I have made when integrating a parallelised implementation of fastECPP into my CM software, which has recently been used to prove the primality of a number of record size 50000 digits