I think you are underestimating how hard the primer needs to be “poked” to go off. It’s metal that has to be deformed, and when firing the gun’s hammer strikes the primer HARD. You shouldn’t be shaking and agitating ammo boxes anyways, and nothing short of dropping an ammo box from significant height would generate enough force to set off a primer, even if a bullet tip happened to be lined up with a primer just right.
To trigger the primer, setting off the bullet, you need a fairly sudden collapse of the primer. Unless a considerable amount of weight were resting on a single bullet, and that bullet’s primer were somehow pressed against a sharp point such that all of the weight was borne by the point on the primer, and someone gave the box a violent enough shake to collapse the primer, nothing would happen.
The odds of this happening are for all practical purposes zero.
To add on to the comments below, there’s only one instance that I know of where a bullet tip can set off another round.
If you look at rounds designed to be fired from lever action guns, you will notice that they all have flat or round nosed bullets. This is because in a lever action gun, the magazine is a cylinder underneath the barrel. The rounds get stacked on top of each other, nose to primer. If the gun’s recoil is sufficiently powerful, or you drop the gun from high enough onto the buttstock, the nose of a pointy bullet could pierce the primer of the round in front of it, and so on and so forth, causing a chain reaction of rounds going off inside your magazine tube.
But even then, the round won’t fire the way you might think it would. A round spits out a bullet forwards because the entire round is sitting inside the gun’s chamber. Think of it as sitting inside a torpedo tube. When the gunpowder ignites, the chamber contains the pressure. Assuming the gun is in good working order, the only direction the pressure can physically go is forwards, and that is what drives the bullet down the barrel. If you take a blowtorch to a round sitting out in the open, it’ll actually just kind of “pop” like a firecracker as the side of the casing ruptures and releases pressure.
Others have explained things pretty well, but one last point: it’s extremely rare to have a huge box of unfired cartridges that are randomly oriented. Factory packaging for ammunition is designed to hold the rounds in a specific orientation. There are various ways to do this, such holding them in a pegboard-like plastic or cardboard tray, or having smaller inner boxes of 10 or so rounds. For military use the cartridges may be held in stripper clips, magazines, or belts which keep them confined and oriented in the same direction as well as being ready for immediate use. Which ever way it is done, the packaging is designed so that the bullet tips cannot impinge on the primers of other rounds in the larger boxes.
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