  The FastECPP algorithm is currently the fastest approach to prove
theprimality of general numbers, and has the additional benefit of
creatingcertificates that can be checked independently and with a lower
complexity.This article shows how by parallelising over a linear number of
cores,its quartic time complexity becomes a cubic wallclock time complexity;and
it presents the algorithmic choices of the FastECPP implementation inthe
author's \cm\ software (https://www.multiprecision.org/cm/) which has been
written with massive parallelisation over MPI in mind, and which has been used
to establish a new primality record for the "repunit" $(10^{86453} - 1) / 9$.
