I really love some of the answers here about slam fires and primers and the term "primer softness".
Remington ran Lake City Army Ammunition Plant from 1941 till 1985 and "NEVER ONCE" loaded a single CCI #41 or 34 primer. Remington was developmental in the type of primer used in the M16 rifle. The highest probability of a slam fire on a M14 or M16 rifle is when a single round is loaded "WITHOUT" the magazine in place to slow down bolt velocity. The military lightened the firing pin on the M16 to help prevent this from happening and reduced the odds of this happening to one in ten million chance. And this is without the magazine in place.
Any primer with a cup thickness of .025 is all you should use in the AR15 rifle.
Below, proper primer seating with a slight primer crush, please note the primer is well below flush with the base of the case.
CHOOSING THE RIGHT PRIMER - A PRIMER ON PRIMERS
Primer Info & Chart + Milspec Primers for Semi-Autos & Other Primer Applications
If you would just read the history of the M16 rifle you would learn a little, in the book below there is a section about slam fires, primers and firing pins. The vast majority of slam fires are caused by reloads and primers not seated to the proper depth. The 5.56 primer is to be seated at least .008 below the rear of the case the same as the 7.62 is.
I use Remington 7 1/2 primers for my general purpose blasting practice ammo and CCI BR4 primers for my accuracy loads.
Now look at the flash photos of the small rifle primers at the link below, the Remington 7 1/2 primers are called "mini flame throwers" and very good for lighting off the Winchester ball powders loaded at Lake City.
The Rifleman's Journal: Primers - Small Rifle Primer Study
Below is the milspec drawing and information for the 5.56 case dimentions, with the primer pocket dimensions, this means the Remington 7 1/2 primer should be .008 to .012 below the surface of the case when seated properly.
Below the 7.62 primer is to be .008 below the base of the case, left center of drawing.