Are good ideas rare?

And are prime numbers rare?

If there are infinitely many ideas, and infinitely many good ones, then... there's just an infinity of both. So, if both sets are countably infinite, then they have the same size. Good ideas aren't rare in that sense.

Ditto for prime numbers. There are infinitely many of those too, and infinitely many integers. So, there are as many primes as there are integers. Prime numbers aren't rare in that sense either.

However, that's only true if you talk about primes and integers in the abstract.

If you look at the number line, primes do get rarer. And, if you alter primes using familiar operations (adding, subtracting, multiplying, dividing), you almost always break the prime, turning it into a non-prime (aka "composite") number.

There's no number line for ideas, but you can talk about altering good ideas in familiar ways (adding, subtracting, switching parts of it), and this usually breaks the idea, turning it into a non-good (aka "bad") idea.

So, in this sense - perturbation by familiar operations - primes and good ideas are rare. Or, not "rare", but easy to break. As David Deutsch would say, they're hard to vary.

Actually, good ideas are rare. There may be infinitely many of them in the set of all ideas, but consider a different set: the set of variants. In that set, good ideas are indeed rare.

There may be infinitely many ways to design an excellent computer, but most ways of changing a good design will just break it.

Maybe yet another way to put this is: good ideas aren't rare, but good variations or alterations are rare.