Using GMP, assuming it all fits in memory and GMP scales fine, it's only 1.8 billion years to finish BPSW.

My single threaded Primo calculation came out to only exp( 4.01 * (log(3140000000000)-log(2000)) + log(2313.8) ) / 60 / 60 / 24 / 365.25 = 550528055283376774128261550300497 years. Based on timings from a few years ago to compute various sizes up to 2000 digits, and assuming of course that we can just handwave practicality and scaling.

AKS using Bernstein Theorem 4.1, about 5e59 years. But parallelism is trivial, so that will really help a lot.