Thank you for your great work.

I’m lisp newbie and I’m using your blog to learn Lisp.

You’re missing the point. O(sqrt(n)) is the order of growth for (prime? n) not for your function (search-for-primes from to).

Rewrite search-for-primes so it outputs not only prime number, but also time elapsed during its testing of this particular number. F.e. (below s-f-p version takes 2 args - start point and how many primes to find) :

> (search-for-primes 100000000000 3)
100000000003 is prime, testing time = 0.1 sec.
100000000019 is prime, testing time = 0.088 sec.
100000000057 is prime, testing time = 0.087 sec.
Done
> (search-for-primes 1000000000000 3)
1000000000039 is prime, testing time = 0.282 sec.
1000000000061 is prime, testing time = 0.282 sec.
1000000000063 is prime, testing time = 0.283 sec.
Done
> (search-for-primes 10000000000000 3)
10000000000037 is prime, testing time = 0.899 sec.
10000000000051 is prime, testing time = 0.89 sec.
10000000000099 is prime, testing time = 0.891 sec.
Done

Sequence 0.09 - 0.28 - 0.9 fits theory quite good.