Viewed about 9 bullseyes shot by a fellow range member with one of his more accurate rifles. He'd removed the threaded muzzle brake on the rifle and made a new end piece for the threaded end of the barrel. He was playing around with reloads to compare velocities between those shot with a muzzle brake and those w/o it. He always chronographs his shots.
Anyway, he showed me the nine 100 yd bullsyes he'd shot. Only difference in his reloads that day was the primer. Different primer for each bullseye and 4 rounds fired at each one. While the groups on his 8 bullseyes were all decent, there was a noticeable difference in them. Each kind primer also provided a different range of velocity.
Darn if I can remember all the brands of large primers used but about the only one he'd didn't use was the Federal Gold Medal bench rest one, did have the std Federal primer. Had other brand benchrest type, magnum and standard primers.
So, his test showed a primer did make a difference for him anyway. I'd done a similiar test some time ago, but used maybe half the kind of primers he'd used. For me, after shooting 3 rounds with maybe 5 different primers, I had a 1/2-3/4" wide hole maybe 2 1/2 or so inches long on my 100 yd target. Each primer had hit at a different spot on my target.