Primitivus is named as "fellow presbyter" by Cyprian here, but it is unclear whether he belongs to the clergy of Rome or of Carthage.
The election of Cornelius in Rome was contested, so the support of the African bishops, especially Cyprian, was important for him. This is why Cornelius was annoyed that the clergy of Hadrumetum addressed their letters to the presbyters and deacons of Rome, and not to Cornelius, as if not accepting his election. Cyprian reassures Cornelius that the presbyters of Hadrumetum were not informed about the decisions of Cyprian to support Cornelius, and the will refer to him from now on.