You might want to start reading at http://mathworld.wolfram.com/PrimalityTest.html. It's only recent that someone discovered a "efficient" algorithm to determine the primality of a number. But it's still an algorithm that's bounded by the 12th power of the number of bits the number is written in. There are faster algorithms, but they either may give false positives, or false negatives. You may want to look into the Lucas-Lehmer test: http://mathworld.wolfram.com/Lucas-LehmerTest.html

You should realize that this is not a trivial problem.

Abigail

In reply to Re: Finding Primes by Abigail-II
in thread Finding Primes by Tommy

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