Comment by SamBam

The point is, with a constructed transcendent number, you can represent any series at all, so long as you have "enough precision."

That last part means you can simply adjust your precision to your desired constraints. If you want to unambiguously represent the primes up through all the four-digit primes, simply change your padding accordingly: 0.000200030005....

Obviously the Buenos Aires Constant in the article is a neater representation, and relies on neater math. But GP's point was that you can stuff anything at all into a transcendent number.