Most "compact" sequence such that there is at least one prime between a(n) and a(n+1)

[David W. Wilson]

> What would be the minimum required exponent (not theoretically, but
> from numerical evidence?).
> 
> Hugo

Empirically, the smallest exponent e that does not admit two primes between n^e and (n+1)^e for any integer n >= 1 appears to be log(541)/log(52) = 1.59267+