Now the standard algorithm used inindustry is the randomized algorithm for prime http://webster.cs.uga.edu/~boanerg/fall2001/csci6610/Randomized_Algorithms.doc however, recently, a new algorithm proposed by an Indian professor which is a determinstic http://www.cse.iitk.ac.in/news/primality.html However, that new algorithm has great significance in theory, but it won't be adopted by the industry since the randomized algorithm is easier to implement and yields accpetable results nearly all the time. You know industry differs a little bit from theory, in a sense that theory always requires preciseness while a good approximation with high efficiency is more valuable.