less pre calculating possible ?

Hi,

There is a gray line between applications that should be done in software and those done in firmware(e.g.HDL).

FPGAs can implement both; firmware for direct hardwiring of functionality giving maximum speed and software(nios) for slower work that depends on fetch-execute cycles.

Generally, complex slow algorithms are done in software and fast intensive data processing in firmware. So I don't see any reason not to use software to search for the largest prime number so far. In fact all keyboard/display issues that interface with human beings and other creatures can be done in software without speed problems.

In all cases there will be a limit of the finite representation, you can't go towards that infinity of mathematicians.