large twin primes and large gaps between primes represent instances of primes being unusually inhomogeneously distributed. (and generalizations: prime constellations, aloof primes OEIS A096265, etc.)
on the opposite extreme, what ranges of numbers have primes unusually homogenously distributed?
maybe consecutive primes in arithmetic progression (CPAP). large known CPAP, sequences of length up to 10, have spacing 210. by the Prime Number Theorem, spacing 210 is expected around e^210 ~= 10^91 . similarly, spacing 30, CPAP sequences of length up to 6, is expected around e^30 ~= 10^13 . but having found a longest possible such sequences in the expected region, it's not clear how to improve on it or extend it.
what is a "usual" homogenous distribution of primes?
maybe ranges lacking twin primes and large prime gaps.
maybe better to study aberrations in the Riemann zeta function.
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