Well said. A fun way to improve one's intuition for the huge space of primes in the regions that are used in cryptography is to run something like openssl pri

Well said. A fun way to improve one's intuition for the huge space of primes in the regions that are used in cryptography is to run something like openssl prime -generate -bits 1024 (This would give you one of two secret parameters for a 2048-bit RSA modulus.) Here is an example output: 171512683213144641422165911053946068613736141364433791764418217818329805042681574174826781297743340609766353737741548521280185783254625590756752560896455821248403501924867464886010664489035275551178636464876794754383911750620888923620343965444339734253757757361106691647372710935609902417522529107877592063581 Not very easy to guess just because the space in question is limited to "1024-bit primes"! And indeed, that's part of why we use primes that are this big when we still use RSA. They're big enough that the number of possibilities makes them not easy to guess (even given the extra hint of "the secret number you're looking for is one of the factors of this 2048-bit semiprime"). Exponentials are always hard for human intuition. We start with some kind of pattern and it feels like there just aren't that many numbers that would satisfy it. But when you get out to large numbers (even numbers as large as the one above), there just are that many numbers that would satisfy the pattern!