Thematics Of Order -- Discussion

[Joerg Arndt]

* Antti Karttunen <Antti.Karttunen at iki.fi> [Apr 18. 2005 14:00]:
> > [...]
> >
> >I do see the connection you are making with logic,
> >
> No, not really, I wasn't interested about logic when I submitted
> A061858 and the related tables and sequences, but instead, I was
> intrigued by Frank Ruskey's algorithm for generating irreducible
> GF(2)[X] polynomials
> (see http://www.cs.uvic.ca/~ruskey/Publications/GenIrrPoly.htm
> and http://www.theory.cs.uvic.ca/~cos/gen/poly.html )
> and was then wondering whether there's any reasonable way
> to estimate whether an irreducible GF(2)[X] polynomial
> (its binary encoding) is also a prime in N. (See:
> http://www.research.att.com/projects/OEIS?Anum=A091206 ),
> and of course it's here where the carry bits, those little lice of
> binary arithmetics come in picture.
> 

This might be interesting:
\jjbibitem{simdiffpolyint}{Susan Landau, Neil Immermann:
\jjbibtitle{The Similarities (and Differences) between Polynomials and Integers},
1996}
CiteSeer has it IIRC.

So also
http://www.jjj.de/fxt/demo/gf2n/#primefact
 ;-)

-- 
p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0
Life is hard and then you die.