Just to ensure that what's the current day status of the computational capacity and what are it's limitations till date, on several mathematical operations listed below -
1.)Suppose $n$ is any natural number , what's the maximum $n$ we can have if in order to calculate $n!$
2.)let $p(k)$ be the partition of $k$ , how much large can we go with present day computers?
3.) How many ' $a$ ' , $b$ digited number can be multiplied? What's the maximum $a$ and $b$ we can have?
In $2002$ computers were able to calculate and show that $34790! -1$ ( 142891 digits ) is Prime , so how much progress has been made since then ? And specifically in the above mentioned questions?
Please forgive me if this wasn't the most appropriate place to launch the question.
I just found this article: http://fredrikj.net/blog/2014/03/new-partition-function-record/