Mersenne: Fwd: Primitive Trinomial of Record Degree
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
Re: Mersenne: Error rates
This would presumably give rise to a serious problem in which people could simply claim to have done work which failed, and turn up at the server and ask for credit to their user scores. There wouldn't be a reliable way (based on current mechanisms) to cross-check the validity of their claim if the results are incorrect and can't be verified by another user. Jeff Woods wrote: > And if the answer to the above is "yes", then why can't Prime95 be coded > to simply "credit" partial time, and throw the number back in favor of a > smaller exponent, a double-check, or factoring work, instead of > permitting work to continue for another few weeks (or months) that is > likely fruitless? Yours, -- === Gareth Randall === _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Error rates
At 08:24 PM 8/30/02 -0400, you wrote: >There is a lot of interesting data in this spreadsheet. Our overall error >rate is roughly 3.5%. If you have an error-free run, the error rate is >in the 1.4% to 2% area. If you have an SUM(INPUTS) != SUM(OUTPUTS) error >or ROUNDOFF > 0.40 error that is not caused by an approaching FFT >crossover, then there is a 56% chance that your LL test will be no good! Question, then: Assume for the sake of argument that you "watch" your results.txt files, and let's say you had THREE such errors by the time the test was 50% completed. If that 56% figure is accurate, then this hypothetical test is almost certainly no good statistically. It isn't even worth finishing the remaining 50%, is it? Would a "serious" tester try the test on different hardware, and/or would it be worth "saving" the interim files, removing them, and starting over BEFORE submitting this likely invalid result... And if the answer to the above is "yes", then why can't Prime95 be coded to simply "credit" partial time, and throw the number back in favor of a smaller exponent, a double-check, or factoring work, instead of permitting work to continue for another few weeks (or months) that is likely fruitless? I wouldn't throw back a result on just one sumout error, but on multiple ones before the test is completed why are we even bothering to complete it, if we KNOW the result is not only suspect, but highly so? _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Database - truncated lucas_v file available
Hi, Since George added offset & error information to the lucas_v database file, it's grown ... now around 7 megabytes, making it painful to download on an analogue modem link. I've therefore created a "truncated" version of the file. This is the same file but with the information omitted for all exponents smaller than the "double check completed through" value on the status page. The new file is only about 40% of the size of the full version, but contains all the information of interest to people working in active PrimeNet ranges. The file is available as follows: http://lettuce.edsc.ulst.ac.uk/gimps/lucas_va.zip or by anonymous ftp from the same host, look in directory /mirrors/www.mersenne.org/gimps It's generated by a cron job run at 0630 GMT daily, if the lucas_v.zip file on the master database has been updated during the previous day. BTW this file has been generated by an open-source compression program which is supposed to produce files 100% compatible with Windows Zip format. Please let me know if there are any problems with decompressing it. The orginal file remains available; omit the last "a" in the URL given above. Regards Brian Beesley _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Still unable to communicate with server.
On Friday 30 August 2002 20:59, I wrote: > Are we losing users? Well, if users can't connect to the server, they're > going to be discouraged. Ditto anyone still using Windows 95 - Prime95 > v22.3+ has problems since George apparently upgraded his development kit. I'm please to report that Prime95 v22.8 runs without problems on my reference Win 95 system (original version + SP1 + assorted patches). Regards Brian Beesley _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: roots of two
I try to make an integer DWT (I already write a NTT that works) . I use the prime number : 3221225473=3*2^30+1 ; the primitive root is 5 ; the order of 2 is 3*2^28. Are there Nth roots of two for each prime of the form p=k*2^N+1 ? How can we quickly find a Nth root of two ? Yan Naessens MPSI Lycée Fauriel Saint-Etienne _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
