If everyone got a unique prime number and a running total vote product was available, I always thought this would be a neat solution. Still susceptible to the goon-with-a-wrench technique I think
That doesn't sound like it secures anything. I can't verify that my prime number is unique (I vote for A. There is already a vote for A at 3. The machine logs a vote for B at 5 and reports to me my number is 3). So it'd be a scheme where nothing can be proved to me that I didn't already know. I still have to trust all the same middlemen, and I don't gain any knowledge about the integrity of an election.
That is an unreasonable assumption, there isn't a secure way to issue everyone with a guaranteed unique prime. And even if there was, what is this system supposed to be doing? It doesn't secure anything and it doesn't enable any new knowledge that wasn't already available by just signing ballots with your name (which is a bad idea, so by comparison we might expect that this prime scheme is also a bad idea). Are you sure that is an interesting thread to pull? It doesn't look at all promising to me.
