This will give you a good background on primers. I think this is about the fourth time I have share this link this week. I'm not saying primer selections are unimportant, but I am saying that beginners have much more important things to master before they can find the difference in primers when running a factory rifle.
https://www.snipershide.com/shooting/threads/a-primer-on-primers.6936610/
Again, I realize you are new here, but try and give as much background detail as possible when asking questions. It gives you a more filtered set of answers in topics that can run wide.
When you say factory barrel, are you talking about some sort of hunting/carry rifle or a match gun?
ETA: OP says this is a Savage factory Palma. The chamber specs are not clear, but the Savage page says the bbl is a 30" button in 1:13 twist.
If you don't know the chamber specs, that is okay but try to share the bbl length, twist, and section?
For example, I have a Remington 700 with a 20" heavy bbl 308WIN with factory chamber/bbl with a 10 twist.
Or, I have a Browning XBolt with a 22" in 12 twist.
Then you may also want to share what your goals really are, will you be shooting this in a Palma Match. Give better detail and background, and you will get better advice.
If you are up to speed, stop reading here. If you are really still leaning, then....
Unless you are running the same pattern rig the Palma team was running when they played with the differences between LRP and SRP, then you may want to slow down and take it from the first chapter instead of jumping to the PhD section. Their reamers and bbls were specific to their loads and brass.
It takes a match rig context to find the difference that created SRP Palma brass. Otherwise, rookies should start with good quality LRP brass and avoid running ball powders in cold weather till they know what they are doing.
You are clearly not discussing a Palm with their reamer, so try not to obsess over their Palma loads unless you are actually running an International Palma Team chamber. You would know it if you had one. This has little or nothing to do with your primer selection so far.
Not to deride a factory rig before I know what you even have, but the primer is probably the least of your concerns as a beginner.
Using Palma brass with small rifle pockets isn't the place to start a factory barrel hunting rig when learning the ropes. This is because we may want to run it in cold weather. Our focus is not on worrying about primer pockets getting loose or the same topics that the Palma Team was working when small primer 308 WIN brass became a thing.
You can still do better than 1.25 MOA with this SRP brass, but it will start with a bullet the gun likes and an extruded powder to make ignition easy no matter what primers you have.
Try to avoid running ball powders with small primers in cold weather. If you must, then use magnum primers like the CCI450 or similar.
Try to run a good quality extruded powder in LRP Lapua brass before you try small primers or ball powders.
Try a different bullet sooner rather than later.
Good Luck and Happy New Year!!!
