That is a great system, but there could still be coarcion to show your "prime number" token to someone, say your employer. Probably not common in the US or the EU, but in Venezuela for example there is a lot of pressure for employees of state owned companies to vote for the government and they use many tactics to make sure you do. I'd be worried about making it simpler for them. Maybe there's a way of addding an extra layer of security?