The aim of this report is to explain the implementation of the elliptic curve primality proving algorithm of Atkin in a distributed way. We describe the use of a Le_Lisp program managed by a bunch of script-shells that run processes on different workstations communicating via the distributed file system NFS. As a result, the primality of 700-digit numbers can be done routinely in about a week of CPU on 10 SUN's. Using twelve SUN's and one month and half CPU, the author was able to prove the primality of a very large number (1065 digits) . This is (up to now) the record for the largest number ever tested for primality by a general purpose algorithm.