on the randomness of primes
- As a "layman's version" of the Green/Tao proof on arithmetic
progressions of primes, I found one of the user comments at
If primes were distributed "randomly" throughout the integers, one
would certainly expect infinitely many twin primes. Interestingly, the
Green-Tao theorem alluded to above (caveat: I haven't read the paper
so only know about the argument by hearsay) gives a precise sense to
the assertion "the primes are distributed in an approximately random
way" and shows that ANY sequence of integers which is "approximately
random" in their sense contains arbitrarily long arithmetic
progressions. In some sense, their theorem is not really a theorem
about primes at all.
Can anyone give a slightly less layman-like description of the
Green/Tao proof and tell me more about what they mean by "random way"
and so on? Or, alternatively, correct this "layman's version" and
tell me what the Green/Tao paper really proved?