Well, that's true if by "computable" you mean "possible to compute in practice in the physical universe" rather than "possible for a Turing machine (or the λ-calculus, etc.) to compute." But usually we use "computable" for the second class, not the first. In particular, you were using it to mean "possible for a Turing machine to compute" rather than "possible to compute in a physically realizable computer" when you said that classical computers are just as capable of performing protein-folding calculations and factoring as quantum computers, only more slowly. In fact, it is straightforward to construct factoring problems that cannot be performed by physically realizable classical computers by any known algorithm because it will take longer than the lifetime of the universe — or, at least, the matter in it.

To be concrete, the current factoring record is RSA-240, a 795-bit number that was factored in November. This required about 2.37 × 10²³ steps of computation by my calculation, and was completed in 4000 core-years. I'm not sure how long it took in real time, nor do I remember how parallelizable GNFS is (I seem to recall it has a bottlenecked step.) To take a thousand times as much computation, you need a 1048-bit semiprime; for a million, 1344 bits; for a thousand million, 1685 bits (which, you'll note, gets us close to the age of the universe on one core); for 10¹² times as much, 2075 bits (close to the age of the universe on a thousand cores); for 10¹⁰⁰ times as much, 43687 bits. The Eddington number is that there are about 10⁸⁰ baryons in the observable universe, so if your computing cores are larger than a single proton, it will take you at least 10²⁰ times those 4000 core-years to factor a 43687-bit number with GNFS, that is, about 4 × 10²³ years.

import math
nfsln = lambda ln: math.exp(((64/9)**(1/3)) * ln**(1/3) * math.log(ln)**(2/3))
nfsln(43687*math.log(2))/nfsln(math.log(
12462036678171878406583504460810659043482037465167
88057548187888832896668011882108550360395702725087
47509864768438458621054865537970253930571891217684
31828636284694840530161441643046806687569941524699
3185704183030512549594371372159029236099
))

But that's still a relatively short time; yes, it's 10¹³ times longer than the universe has existed so far (and 10¹³ times longer than it will exist if the Big Rip happens, and about 10¹¹ times longer than it will exist if the Big Crunch happens), but it's possible that the universe might last longer than that. The Stelliferous Era is due to end in 10¹⁴ years, so that's a billion times longer than the Stelliferous Era will last, but red dwarfs will continue burning and providing power for another hundred times that long. Still, though, new red dwarfs will be formed from time to time, and perhaps they could power your classical computer for long enough to factor that number.

Skipping over the Black Hole Era (can your computer survive the Black Hole Era?) all the black holes are conventionally predicted to have decayed via Hawking radiation in about 1.7 × 10¹⁰⁶ years. So a semiprime of 161133 bits, which will take about 2.37 × 10²⁰⁶ operations to factor with GNFS, cannot be factored in that time with the GNFS on classical computers as long as every Xeon-speed processor is bigger than a baryon.

But wait! Maybe your processors can run faster; at the scale of nuclear reactions, a Xeon's few GHz is unimaginably slow. But there's still a speed limit: you can't realistically do more than one operation per Planck time, about 5.4 × 10⁻⁴⁴ seconds. So you can maybe get a speedup of up to about 10³⁵ by making your smaller classical processors go faster, using digital logic mechanisms yet unknown, perhaps shockwaves traveling around a neutron star or something. (All the nuclear reactions we know about run enormously slower than this, though.)

Well, if you can run your proton-sized processors at 10⁴⁴ Hz, that means that by the end of the Black Hole Era you can factor a semiprime of 240857 bits or so on a classical computer.

So that's probably pretty much the limit in the physical universe.

If you can build a quantum computer, using Shor's algorithm, you can factor such a number in about 833586709574 operations (8.3 × 10¹¹) times whatever the constant factor is.

shorln = lambda ln: ln**2 * math.log(ln) * math.log(math.log(ln))
shorln(math.log(2) * 240857)

So, while you can definitely factor a 240857-bit semiprime on a Turing machine, which is a theoretical construct, you cannot factor it on a physically realizable computer — unless we can build a large quantum computer (one with almost half a million qubits), in which case we can do it in, probably, a few minutes.

In conclusion, either your use of "computable" and "CC" in your original comment referred to computability in a particular family of abstract models of computation, not in physically realizable classical computers; or your statements in that post about the relative computing power of classical and quantum computers were simply mistaken with respect to current knowledge, because (assuming QCs are physically realizable) physically realizable QCs can compute things that physically realizable CCs are not known to be able to compute.

I say not known to be able to compute because the question of whether BQP = P is still undecided. It might turn out that classical computers can simulate quantum computers in polynomial time, thus providing a polynomial-time algorithm for factoring — although this is unlikely, we don't have a proof that it's impossible. Even if BQP ≠ P, it's possible that integer factorization is in P, and we just haven't found an efficient algorithm for it yet, despite thousands of years of trying. But it's not the way to bet.

It is of course correct that it would be an enormous and improbable breakthrough for someone to find a way to build a physically realizable computer that can compute things that an abstract, theoretical Turing machine cannot. That would be a counterexample to the Church–Turing thesis.