Richard Brent says he sent this to the list, but I haven't seen it here yet so I assume it was blocked (maybe by the subscriber-only filter?)
Colin Percival >From: Richard Brent <[EMAIL PROTECTED]> >Date: Tue, 3 Sep 2002 16:39:50 +0100 (BST) >Subject: Primitive Trinomial of Record Degree > > Primitive Trinomial of Record Degree > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >We are pleased to announce a new primitive trinomial of record degree >6972593. >The trinomial, over the finite field GF(2), is > >(A) x^6972593 + x^3037958 + 1 > >It was found on 31 August 2002 on a Sparc Ultra-80 in Oxford. >The previous record degree (by the same authors, in August 2000) >was achieved with the trinomial > >(B) x^3021377 + x^361604 + 1 > >The degree 6972593 is the exponent of a Mersenne prime M6972593. Thus, >in order to show that (A) is primitive, it suffices to show that it is >irreducible. This takes 16 hours on a 500 Mhz Pentium III with our program >"irred". The method is described in: > > R. P. Brent, S. Larvala and P. Zimmermann, "A fast algorithm for testing > reducibility of trinomials mod 2 and some new primitive trinomials of > degree 3021377", Mathematics of Computation, to appear. Preprint available > from http://www.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub199.html > >Because the trinomial (A) is primitive, the associated linear recurrence > >(C) x[n] = x[n-6972593] + x[n-3037958] (mod 2) > >has period M6972593 = 2^6972593 - 1. This leads to random number generators >with extremely large period and good statistical properties. > >One larger Mersenne prime (M13466917 = 2^13466917 - 1) is known >(see http://www.mersenne.org/status.htm). It is easy to show, using >Swan's theorem, that there are no primitive trinomials of degree 13466917. > >We have now completed 53% of a complete search for primitive trinomials >of degree 6972593. The search commenced in February 2001 and has taken about >100,000 mips-years so far. Further information on the search for primitive >and "almost primitive" trinomials (that is, trinomials which have a large >primitive factor) is available at > > http://www.comlab.ox.ac.uk/oucl/work/richard.brent/trinom.html > >We are grateful to the following individuals and organisations for their >assistance in providing computer time: > >Nate Begeman >Nicolas Daminelli >Brendan McKay >Barry Mead >Juan Varona >Australian National University Supercomputer Facility (ANUSF) >Australian Partnership for Advanced Computing (APAC) >Centre Informatique National de l'Enseignement Superieur (CINES) >INRIA Lorraine >Oxford Centre for Computational Finance (OCCF) >Oxford Supercomputing Centre (OSC) >Oxford University Computing Laboratory (OUCL) > > Richard P. Brent > Samuli Larvala > Paul Zimmermann > 3 September 2002 _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
