Proven Primes

[Tim Dierks]

At 10:04 AM 3/7/2003 +0000, Ben Laurie wrote:
>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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