Yep. Fire departments don't like primers inside metal cans. If the box heats up enough, then all the anti-sympathetic detonation packaging is no longer up to the task because the primers get too sensitive for it to work. Simultaneous ignition in the fire can then throw pieces of metal at the firemen. An ammo can is good for smokeless powder as a buckling lid or popped latch or seam should release the gas before a real explosion occurs. But with primers the gas is generated too fast for that to work reliably.
Get a soft plastic storage container or a bread or cake box, then use a sealable bag and desiccant around the primers inside. You can go bag-inside-bag if you want to and use a heat seal if the primers are going to be there for a long time. If you buy them in cartons or slips of 5000, those are great candidates to go straight into plastic bags with a desiccant before they're even opened.
One thing to note with most desiccants is that as they become saturated with water, water escapes by re-evaporation at an increasing rate until they reach equilibrium (capturing and releasing at the same rate) at the saturation temperature, so the relative humidity they allow in the container increases. It doesn't matter if its clay, silica gel, or rice. You want it as bone dry as possible when you put it in the container. Up to about 20% RH, the clay will have the most capacity. Above that, the silica gel has slightly more capacity. I don't know how rice compares.
If you are drying primers out, consider a two-step process where you put a fair amount of desiccant in on the first pass to collect the bulk of the water from paper packaging and the content. Then replace it with a smaller maintenance quantity of freshly dried desiccant.
The battery-powered humidity meters (built into some thermometers, too) can be kept in a bag with them to monitor RH. Silica gel has often has cobalt chloride as a color indicator, which is convenient, but the clay and rice will swell visibly with saturation, which is another indicator.
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