You sometimes hear bout these huge prime numbers (RSA prime number challenge comes to mind) and I was curious about what algorithms or formulas prime-number generators use in practice ? For example in cluster / cloud computing, parallel computing ...etc.
I imagine that everyone has their own "custom" optimized versions of more known prime number generational algorithms but what are the "base methods" used to do so.
Thank you very much in advance !
edit: I hope that I used the right [tags].