One way to tell how we can safely store primers is to look at the stringent federal hazardous materials regulations for packaging and shipping.
Check out 49 CFR, Subpart 173.62, packing instruction 133. This provides the federal requirements for packaging Primers, Cap Type, UN0044 (i.e., ALL small arms primers that we the public use).
According to the reference above, primers MUST be packaged in a certain way, but choices are allowed within certain parameters. For example:
(1) Inner packing consisting of "Trays, fitted with dividing partitions" is one option, and happens to be what you and I are accustomed to seeing.
(2) The reg above requires that if the primers are housed in trays, as mentioned in (1), then intermediate packagings are required. Sooooo, we follow the link above to page 11 of the PDF, look at the "Intermediate packagings" column for packing instruction 133, and see that we can store the tray of primers in a receptacle made of (our choice) fiberboard, wood, plastic, or METAL.
(3) Finally, the regulation gives us a choice of outer packagings, noted in the 3rd column of the same page 11 of said PDF-- steel box, aluminum box, wooden box, plywood box, and plastic box, among others.
Despite the reasoned arguments of some above, wncchester has it right. Ammo cans are a good, legitimate way to store primers, as are wooden boxes, cardboard boxes, fibreboard boxes, and plastic boxes.