Lets suppose a brute-force algorithm testing all numbers up to n. (don't wanna complicate it by restricting it to primes)

After a week and testing 10^x numbers you'll get 2 correct Wieferich primes and the information that calculating a third prime bigger than 10^x takes at least 10^x steps.

That's an empiric lower bound for the complexity, you can tell that this brute-force approach is at best O(n) for n<10^x, which is quite accurate!

OK, this example is a little bit too trivial, since it's a decision problem.

You actually have 10^x points and not only 2 !

Cheers Rolf

In reply to Re^6: Algorithm complexity by LanX
in thread Algorithm complexity by fauria

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