According to the TSA, it's not prohibited to place primers in carry-on baggage **IF** they are properly packaged.
Ammunition primer caps aren’t prohibited
in checked luggage on airlinesThe Transportation Safety Administration said Wednesday that the ammunition
primers are not prohibited in checked luggage but must be packaged correctly.
Checking the packaging is the responsibility of the airline, the TSA said.
https://www.enterprisenews.com/story/news/crime/2010/12/30/ammunition-primer-caps-aren-t/40207501007/This story is from 2010, so it may be dated. Also, each airline can have its own prohibitions beyond that of TSA.
I checked the TSA website and found no mention of transporting primers via commercial passenger planes.
Black powder is considered an explosive and is prohibited. If primers were forbidden, they wouldn't allow ammunition packed in proper containers, would they? Each primer is seated in a cartridge primer pocket and in divided containers to prevent accidental damage causing them to ignite. If you package your primers similarly to prevent accidentally striking them, it should be okay.
I would place them in a padded hard-sided case similar to the kind you'd place your firearm in. That should be safe enough to prevent damage from clumsy baggage handlers and conveyor belts.
When in doubt do your own research and ask your airline.
Hawaiian says this about ammo:
Rule 18 - D.1.a.
ii. All ammunition must be packed in the manufacturer’s original packaging
or securely packed in a fiber, wood or metal container suitable for travel.
Furthermore, the ammunition inside the container must be protected
against shock and secured against movement.
iii. All ammunition must be packed separate and apart from any firearm
unless the firearm’s case has a designated storage space for ammunition
that secures it and protects it from shock and movement.
https://www.hawaiianairlines.com/legal/domestic-contract-of-carriage/rule-18"Protected against shock and movement" ought to suffice for primers, too.
This is my opinion. Make 100% sure before you travel.