Primus is apparently the nickname of the 1st Viper Squadron of the Colonial Fleet.
William Adama was a member of this fighter group, in addition to other pilots from the Cylon War era such as Raymond Lai. The logo of this group is adorned prominently on the nose of many restored Viper Mark II fighters that were to occupy the Galactica Museum.
A photo of a younger William Adama and his two boys, Zak and Lee, shows the Primus logo on his jumpsuit and his old fighter, Viper 7242.
Adama's long time friend, Saul Tigh, apparently was a member of the fighter group known as the Vigilantes.