It’s a very generic question. Why are you asking it???<p>Let’s try to give some information. First read Wikipedia: <a href="http://en.wikipedia.org/wiki/Prime_number" rel="nofollow">http://en.wikipedia.org/wiki/Prime_number</a><p>> Why are large prime numbers important?<p>Pehaps I’m biased, but IMHO: <a href="http://en.wikipedia.org/wiki/Prime_number#Fundamental_theorem_of_arithmetic" rel="nofollow">http://en.wikipedia.org/wiki/Prime_number#Fundamental_theore...</a><p>> What is the largest one found?<p>List at the bottom of the section: <a href="http://en.wikipedia.org/wiki/Prime_number#Special-purpose_algorithms_and_the_largest_known_prime" rel="nofollow">http://en.wikipedia.org/wiki/Prime_number#Special-purpose_al...</a>