Long ago I experimented with 3,5 and 10 shot groups.If you shoot 5 to 6 three-shot groups with a given cartridge and rifle, you're probably gonna see a 4X spread in their sizes. 10 shot groups are better. I prefer 20.
How much does our shooting skills effect the group sizes?
I give credit to tool and die maker Ferris Pindell of Sierra Bullets in the 1950's for convincing them (and top ranked benchrest shooters) to full length size their fired rimless bottle neck cases setting shoulders back a couple thousandths. Case necks end up better centered on case shoulders, the part of the case that centers the neck and bullet in the barrel when fired. Mr. Pindell is one of the "P's" in the PPC family of cartridges.
My first "ladders" are 5 shot groups. As the loads are refined,I finally settled on an average of 10 five shot groups as my final test of a load or rifle.
I thoroughly clean the bore between groups, and I fire a single "fouling" round into the berm before shooting each group.
My results are similar to yours as far as standard primers and neck sizing go.
The exception is belted magnums. Usuaslly, but not always, groups in my belted magnums benefit from Remington 9 1/2 M magnum primers.