Plus, the (known) large ones are all of a nice enough pattern that you could almost factor just by looking at the digit count of the product.

Or by finding them in one of the lists of largest known primes. :-)

Yes, sorry, the implicit assumption I accidentally left in my head is that when we're talking about factoring being important, it's products of 2 biggish primes (hence an answer one step removed from the lists of largest known primes).