If we assume that prime number distribution is COMPLETELY random (subject to 1/log(x) restriction), can we prove twin prime conjecture or Goldbach conjecture ?
My feeling is that, this will be trivial for twin prime conjecture, but how to give a rigorous proof ? Does "completely random" imply that there will be infinite twin primes ?
On the other hand, if prime number distribution is completely random, will Goldbach conjecture still hold true ?
For example, if we consider all numbers between 1 and 100, if we assume prime number completely random distribution, will Goldbach conjecture still hold true For this set of numbers ?
The reason I ask this question, because, people often said that "primes behave almost completely random except subject to 1/log(x) restriction".