Re: Prime gaps

[Gerhard Niklasch <nikl@mathematik.tu-muenchen.de>]

In response to
> Message-Id: <199804252102.RAA12680@monk.mps.ohio-state.edu>
> From: Ilya Zakharevich <ilya@math.ohio-state.edu>
> 
> The current limit of primes 436e6 is related to a prime gap >255
> appearing near this number.  When the gap >511 appears first?

After 1999066711391.

(According to Henri Cohen, ACiCANT, Section 8.1, Implementation Remark 1.)

> Is it possible to have a not backward-compatible primediff which will
> keep gaps/2 ?  Then the theoretic limit will move to 4e9 on 32-bit
> machines, and this may be lifted if initprimes() takes a double as a
> limit... 

Should be possible in principle, but it seems to be of limited
usefulness, except for some highly specialized applications.
The parts of PARI which heavily depend on the diffptr table
(factoring, arithmetic functions, Euler products and the like)
are usually quite happy with the default setting at 500000.

Enjoy, Gerhard