In the past, I have used whatever I've had the most of in one lot... for the purpose of consistency. Mostly, I have used Winchester and Remington primers over the years with no problems. I know that some target shooters went with the Federal Match primers. I tried them but could detect no advantage or difference with them other than being a little more expensive and a little harder to find. Sometimes simple nomenclature sells I guess. Not that long ago, many in the accuracy game were using standard LR or SR Remington primers. I have a good supply of bricks of Remington standard LR primers for standard LR loads, have used a bunch of them for all manner of standard loads and cartridges and have never had an issue.
For big magnum cases I have drifted over to CCI #34s. CCI designed them for military type ammo where slam fires were a potential with either dirty or slightly out of time auto loaders. By chance, along the way I stumbled upon some info about the CCI #34 primer stating that it had the same amount of poop and compound as their Magnum primer- huh? Makes sense for severe conditions use military ammo especially that loaded with ball powder- OK. I tried some in a couple of large magnum cartridges and- OK huh- worked fine! Also by sheer chance I discovered the CCI #34 primer worked best in one individual bolt rifle that had, at the time, a weak striker spring and would occasionally fail to fire with other primers like Win and Rem. Another- huh?- On the surface that didn't make sense. I have since replaced the weak spring which fixed that issue but that experience pointed to the odd conflicting situation of....
easier to ignite but harder to (slam fire) ignite CCI #34- huh? Not sure about how to reconcile that conundrum other than maybe the compression specs of the compound and anvil in the #34 along with the cup specs allow for a better pin strike in the particular case I was loading in the rifle with the weak spring... I dunno? Nonetheless, that experience pointed to the basic reliability of ignition of the CCI #34 so now that is my primary LR Mag primer. I was able to build a large supply of CCI #34s along with an already large supply of Rem and Win standard LR primers before the latest shortage really took hold.
In April this year I ran into an old acquaintance who probably has fired more reloaded rounds and has as much experience with various calibers as any one I know of, the past editor of one of the largest loading and cartridge reference books on the market. I asked him about the CCI #34 performance and what I had discovered. He immediately said oh yes and was very familiar with the apparent conundrum of the "ignitability" of the CCI #34. He supported my suspicions about the reasons and said he had discussed that very issue with the people at CCI and they confirmed the information. Whoda thunk it!
Right now, given the state of affairs- grab any you can find. They all work
