The existence of a simple probability argument for Goldbach’s conjecture, actually favors the existence of a simple proof. Primes aren’t actually random; if the assumption of randomness already implies the truth of the conjecture with high probability, then a few extra bits of provable structural information about their distribution may be enough to supply a proof.
Yes. But also what works here is not the randomness of distrubution of primes, but the number of attempts (to get a sum of primes) which is implied by any sufficiently large number (N/20. Only very large gaps in prime distribution will be sufficient to disprove statistical proof. There is a postulate that there are no such gaps exist https://en.wikipedia.org/wiki/Bertrand%27s_postulate
Just to be clear, Bertrand’s postulate is actually a theorem (i.e. a known result), not a postulate/hypothesis. It is called a “postulate” for historical reasons.
The existence of a simple probability argument for Goldbach’s conjecture, actually favors the existence of a simple proof. Primes aren’t actually random; if the assumption of randomness already implies the truth of the conjecture with high probability, then a few extra bits of provable structural information about their distribution may be enough to supply a proof.
Yes. But also what works here is not the randomness of distrubution of primes, but the number of attempts (to get a sum of primes) which is implied by any sufficiently large number (N/20. Only very large gaps in prime distribution will be sufficient to disprove statistical proof. There is a postulate that there are no such gaps exist https://en.wikipedia.org/wiki/Bertrand%27s_postulate
Just to be clear, Bertrand’s postulate is actually a theorem (i.e. a known result), not a postulate/hypothesis. It is called a “postulate” for historical reasons.