Try and solve a few problems on hackerrank.com that way. Their cpu time restrictions are usually too stringent for Math::BigInt, even with a "fast" backend. Python ints are built-in, bignum is an afterthought.
Show me a hackerrank problem that can't be solved in Perl because of time restrictions.
The only one I haven't been able to solve in Perl was PRNG Sequnce Guessing, so I solved it in Java. But the problem wasn't the time constraint, but the different behaviour of bit operators on big numbers.
Now that I've had some time to kick it around, this is actually a great example. My Python program solves the sample problem in 1 second. In Perl, using Math::BigInt with the default backend, it takes 10 seconds. With the GMP backend, 5 seconds. With Math::GMP, 1 second, same as Python. By resorting to vile trickery, I was able to get the Perl to run in 0.5 seconds with no modules at all. Here's the kicker, though: the Python program runs in 0.1 second under PyPy (basically JIT compiled Python).
Oh look, it's basically the same problem I solved in my old node, Predict Random Numbers. Fifteen years ago. Back then, there wasn't so much information available online, so I actually had to get on my bike and ride to the Stanford math department library to find that algorithm.
That problem involves 48-bit numbers, which really aren't all that big. Maybe try something in the Number Theory category.
Update: Haha, we didn't have youtube back then either.