The Praetorian Guard are famous for both protecting emperors, and murdering them.
An organisation able to overthrow emperors was obviously large, but what was the size of it when compared to the normal Roman army?
I know this is a broad question, so I'll narrow it down to the reigns of Pertinax and Septimius Severus.
Thanks!
I know you specified Pertinax and Severus, but I'll answer with what I can anyway in hopes that it will aid you some.
Under Augustus, the Praetorian was 9 cohorts of 1000 soldiers each. 3 cohorts stayed in Rome and the other 6 were in nearby cities.
Since you mentioned Severus, an interesting tidbit about him and the Praetorian - he opened the job to all Roman soldiers. Previously, only soldiers from Italy were allowed to join the Praetorian. Source: World Book Encyclopedia 2014
From 'The Complete Roman Army' by A.Goldsworthy:
"Its size was kept at nine cohorts of 480 men, just smaller than a legion. At first only three cohorts did their duty in Rome at any one time, but under Tiberius, all nine cohorts were concentrated in the newly built barracks (the castra praetoria) on the edge of the city. Later emperors would also increase the size of each cohort to military strength."
"Attached to the praetorian was a small cavalry force which steadily grew in size, which along with the emperor's house guards (equites singulares Augusti) reached a peak of 2,000 men at the end of the 2nd century AD."
It was my understanding that the power of the Praetorians came from the fact that they were close to and had access to the Emperor, not so much that they were huge in number.