GMP is installed on many systems now, partly because GCC started requiring it. MPFR is much less common. GMP is a big help for lots of things, but MPFR much less so, and I used it via Math::MPFR so you'd need that installed also. It looks like it is used in prime_count_lower and prime_count_upper for large enough values, and the floating point routines harmreal, ExponentialIntegral, LogarithmicIntegral, RiemannZeta, RiemannR, and Pi. For Pi it's a very small savings vs.the standard GMP back end. But the floating point things like RiemannZeta are just hard to do in Perl or GMP's rudimentary mpf layer (for me at least). Using Math::MPFR (thanks syphilis!) is thousands of times faster than Math::BigFloat even using the fast GMP backend. The MPFR implementors are very sharp and also better practicing numerical analysts than me.
For AWS EC2 machines I usually just install the packages with apt-get or yum. I also do git and clone/build/install the latest versions of my modules but that's because I want the absolute latest. cpan is fine and as long as you have GMP you should just be able to cpan Math::Prime::Util Math::BigInt::GMP. But make sure it did find GMP (try cpan Math::Prime::Util::GMP to check).
14 seconds for Pi to 50k digits... Ouch. Moar fastar! At least it's faster than the default Math::BigFloat (which doesn't have the luxury of dropping into custom C code).
As Discipulus says I should try use integer as well to test the Perl spigot. I usually don't like that pragma because it's signed which is never what I want, but that's not relevent here. Now I'm pondering a digression into how to implement use uinteger. At first glance it doesn't look terrible hard to do in the core, but using a whole new hint bit is unlikely to fly. Maybe a test just to see if it would work...