Indeed. The commonly used one is ECPP which uses elliptic curves cunningly to not only prove primality, but to produce a certificate which can be quickly verified.
Probabilistic prime tests are just that - probable. ECPP actually proves it.
Does anyone, in practice, care about the distinction, if the probability that the prime test has failed can be proved to be far less than the chance that a hardware failure has caused a false positive ECPP test? To restate the question: all calculation methods have a certain possibility of failure, whether due to human or mechanical error, however minute that possibility may be. If I can use a probabalistic primality test to reduce the possibility of error due to algorithm failure to a point that it's well below the possibility of error due to hardware failure, what's the practical difference?
Thanks, - Tim
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