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

[David W. Wilson]

Oh, wait, I meant to say...

Empirically, log(541)/log(52) = 1.59267+ seems to be a lower bound on exponents that admit at least one prime between n^e and (n+1)^e for all n >= 1.

> -----Original Message-----
> From: David W. Wilson [mailto:wilson.d at anseri.com]
> Sent: Wednesday, December 12, 2007 9:25 AM
> To: seqfan at ext.jussieu.fr
> Subject: RE: Most "compact" sequence such that there is at least one
> prime between a(n) and a(n+1)
> 
> > 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+
> 
> 
>