While I also doubt the twins ability to calculate unknown primes, I do think that the article falls prey to many of the same trappings that they are calling out Oliver Sacks for.

While Oliver didn't know math enough to talk about known prime number tricks, the author of the article also clearly didn't know books well enough to include ruling that aspect of the story as false since a commenter found at least a contender for the book, which also opens up the theory that the twins memorized the numbers from a book. To take it a step into theorizing, since it's been shown at least one book existed, maybe others that have been lost to age also existed.

Also, with no proof the article talks about how the twins perceived the numbers, saying "More likely is that they called out the numbers figure by figure" instead of in the extended format. A 25 digit number is only in the septillion area, and numbers follow a latin naming scheme so it's not even that hard to remember. This is comparable to Oliver assuming further numbers were prime with no proof.

Plus there's the fact that this is all in hindsight, I think it'll be fun to look back in 40 years from now and see how the article stands the test of time. Maybe we discover an easy way to calculate arbitrary primes in our head and the original story becomes believable.