From: sfinch@mathsoft.com
Subject: Re: euler's constant
Date: Mon, 10 Nov 1997 13:32:43 -0600
Newsgroups: sci.math

In article <6476m3$kna$1@news1.rmi.net>,
  kfoster@shell.rmii.com (Kurt Foster) wrote:
>
> David Bakhash (cadet@mit.edu) wrote:
> . has it been figured out if euler's constant is rational or not?  Or even
> . algebraic?
> .
>   Nope.  Not last I heard, anyhow.  Best I've heard is, if it's a fraction
> it's got a huge denominator, > 500,000 decimal digits IIRC.  I think there
> are also some results to the effect that, if it's algebraic, its minimal
> polynomial has big coefficients, large degree, or both.

Using Brent's algorithm accelerated by binary splitting, Thomas
Papanikolaou was able to compute 1,000,000 decimals of Euler's constant
and, from this, 475006 partial quotients of its continued fraction,
proving that if gamma is a rational number, then its denominator must
exceed 10^244663.  See the web page

    http://www.mathsoft.com/asolve/constant/euler/euler.html

for more information about Euler's constant and

    http://www.mathsoft.com/asolve/constant/constant.html

for many essays about various mathematical constants.


                                        Steve Finch