Also, for a practical engineering problem, like writing an RSA implementation which will be used in an SSL implementation which will encrypt credit card numbers

Also, for a practical engineering problem, like writing an RSA implementation which will be used in an SSL implementation which will encrypt credit card numbers on an e-commerce website, it is okay to use probabilistic tests which have a tiny chance of a false positive (the test claims a number is prime when it is actually composite). You can generally repeat a probabilistic test with different parameters to make the probability of a "false positive" prime number very tiny -- like .000 000 000 001 -- while still staying within the computational budget manageable on an ordinary computer (obviously, a practical Internet security scheme should be able to complete its computations in a second or two on a typical desktop, laptop, server, and smartphone). So probabilistic tests are good enough for practical purposes, but you need a non-probabilistic test to get the false positive probability all the way down to zero. And you need to use a method that has zero percent false positive chance to claim a world record. The EFF-administered monetary prize for a record-breaking prime number, for example, requires "the primality proof must be a deterministic proof..." [1] So you can't use probabilistic methods. [1] https://www.eff.org/awards/coop/rules https://www.eff.org/awards/coop/rules