@hipsterelectron 🤨 oh dear... I can see I have some catching up to do. (Not least I read a lot slower. And, uh, had mentally cache swapped out all of mathematics after the last few years.)

@d_rift also this book was clearly written by a big NSA prime number fan so i feel really bad recommending it https://archive.org/details/gdelsproof00nage/page/n133/mode/2up particularly because it made me feel hilbert's bullshit might have been vaguely interesting at one point -- i strongly urge you (when you have the time to devote to it--it's not long at all) to read it in the voice of an NSA crypto head who thinks if they prime number hard enough they can defeat god

especially there is an intrinsic give and take between:

1. "serial" enciphering (analogized to formulas of notation)
2. "parallel" DH PRNG extraction (analogized to godel numbering of statements)

they raise goldbach's conjecture offhand once right after mentioning that the even integers are a group but the odds aren't (i guess evens would be a ring, while the primes are an abelian group). the relationship to goldbach's "every even number can be expressed as the sum of two primes" is just DEEPLY fascinating.

the author makes the point that there is in fact just enough room for godel to add a "mirror" big enough to hold the meta-mathematical statements godel made to defeat hilbert

Finally, we suggest constructions of hash functions which we believe
are appropriate to instantiate the random oracle.

finally, we have instantiated the random oracle, from hit sci-fi series "we made it up. you cannot instantiate the random oracle"