Let’s try to give some information. First read Wikipedia: http://en.wikipedia.org/wiki/Prime_number
> Why are large prime numbers important?
Pehaps I’m biased, but IMHO: http://en.wikipedia.org/wiki/Prime_number#Fundamental_theore...
> What is the largest one found?
List at the bottom of the section: http://en.wikipedia.org/wiki/Prime_number#Special-purpose_al...