Thanks to those of you who have provided answers for me. They make sense. When I look again at the: ------- Mersenne Exponent Test Distribution Map ------- at http://www.mersenne.org/primenet/status.shtml I see the counts in the "Avail" columns slowly drop over time as numbers are assigned. But every now and then the Avail counts jump up again.
Would I be correct in assuming that this happens when numbers that have been assigned are abandoned by the person or timed out and taken away by the server? OR are there actually more numbers that become available over time (i.e. as they move from Factoring to LL to Double Check)? OR is there a secret stash of available numbers that haven't all been made available for distribution yet?...well maybe not secret, but numbers that can't be released yet for some good reason. ----- Original Message ----- From: [EMAIL PROTECTED] Date: Wednesday, October 25, 2006 1:00 pm Subject: Prime Digest, Vol 30, Issue 20 > Send Prime mailing list submissions to > [email protected] > > To subscribe or unsubscribe via the World Wide Web, visit > http://hogranch.com/mailman/listinfo/prime > or, via email, send a message with subject or body 'help' to > [EMAIL PROTECTED] > > You can reach the person managing the list at > [EMAIL PROTECTED] > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Prime digest..." > > > Today's Topics: > > 1. Re: Curious recent GIMPS member (Steinar H. Gunderson) > 2. Re: Curious recent GIMPS member (Jason Papadopoulos) > 3. Re: Prime sequence formula, solution to pi(x) (Hans Riesel) > 4. Re: Curious recent GIMPS member (david eddy) > > > ------------------------------------------------------------------- > --- > > Message: 1 > Date: Wed, 25 Oct 2006 11:21:16 +0200 > From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> > Subject: Re: [Prime] Curious recent GIMPS member > To: [email protected] > Message-ID: <[EMAIL PROTECTED]> > Content-Type: text/plain; charset=utf-8 > > On Tue, Oct 24, 2006 at 09:03:29PM -0400, Jason Papadopoulos wrote: > > If you multiply two N-digit numbers you get a 2N-digit product. > > This is called a convolution. If you then insist that the answer > > fit in N digits, then the high-order N digits 'wrap around' and > > get added to the low-order N digits. That's just a property of > > convolutions. > > Well, at least of circular convolutions, but all convolutions > calculated via > the FFT are circular in some sense, so yes. > > > The problem is that when p is big, you want the convolution to be > > performed via FFT methods, and getting the automatic wraparound > > requires an FFT of a prime number of elements. While that's possible > > and even can be made efficient, it's much more efficient to do > > the convolution when the FFT size is highly composite. > > Speaking of which; what kind of FFT does Prime95 compute? (I'd > normally guess > it's a Cooley-Tukey variant, but you never know with George's magical > assembler, and I have no idea about DIT/DIF and radices :-) ) > > > The Discrete Weighted Transform basically does that. It's a way > > to pack a prime number of bits into smaller number of 'words', > > using a 'variable-base' representation. > > Well, there's the magic part :-) But thanks, it's a bit clearer now. > > /* Steinar */ > -- > Homepage: http://www.sesse.net/ > > > ------------------------------ > > Message: 2 > Date: Wed, 25 Oct 2006 07:59:53 -0400 > From: Jason Papadopoulos <[EMAIL PROTECTED]> > Subject: Re: [Prime] Curious recent GIMPS member > To: The Great Internet Mersenne Prime Search list <[email protected]> > Message-ID: <[EMAIL PROTECTED]> > Content-Type: text/plain; charset=ISO-8859-1 > > Quoting "Steinar H. Gunderson" <[EMAIL PROTECTED]>: > > > Speaking of which; what kind of FFT does Prime95 compute? (I'd > normally> guess it's a Cooley-Tukey variant, but you never know > with George's magical > > assembler, and I have no idea about DIT/DIF and radices :-) ) > > If memory serves, it's a radix-4 real-valued Cooley-Tukey transform. > The use of a real-valued transform is a little unusual, almost all > the > other Mersenne-testing programs use a complex-valued FFT that's > adapted > for non-complex data. > > The 'special sauce' in Prime95 is not the choice of algorithm, but > the data layout and the method of shuffling data back and forth to > keep critical information in cache as long as possible. Prime95 also > makes extremely good use of prefetching, overlapping essentially > all main-memory latency with useful work. > > This should still be present, though it's quite dated by now: > > www.mersenne.org/p4notes.doc > > jasonp > > ------------------------------------------------------ > This message was sent using BOO.net's Webmail. > http://www.boo.net/ > > > ------------------------------ > > Message: 3 > Date: Wed, 25 Oct 2006 14:33:20 +0200 (MEST) > From: Hans Riesel <[EMAIL PROTECTED]> > Subject: Re: [Prime] Prime sequence formula, solution to pi(x) > To: The Great Internet Mersenne Prime Search list <[email protected]> > Message-ID: <[EMAIL PROTECTED]> > Content-Type: TEXT/PLAIN; charset=ISO-8859-1 > > Hi, > > I have read your email with some interest. As far as I can see, > your formula resembles that of Legendre. You can find this explained > in the first chapter of my book: Prime Numbers and Methods of > Factorization, 2nd ed., Birkha?ser, Boston 1994. > > Regards, > > Hans Riesel > > > > > > ------------------------------ > > Message: 4 > Date: Wed, 25 Oct 2006 15:36:07 +0000 > From: david eddy <[EMAIL PROTECTED]> > Subject: Re: [Prime] Curious recent GIMPS member > To: The Great Internet Mersenne Prime Search list <[email protected]> > Message-ID: <[EMAIL PROTECTED]> > Content-Type: text/plain; charset="iso-8859-1" > > > > On Tuesday 24 October 2006 19:18, david eddy wrote: > > > > > > what happens when a LL test is proved wrong? > > > > > Brian Beesley wrote: > > Hmm ... the LL test is never wrong, it is a mathematical theorem! > > > > However computations performed in a computer can (and sometimes > do) go wrong, > > for a number of reasons. > > The important reason a LL-test goes wrong is due to > using floating point FFT to perform exact integer arithmetic. > > It is fortunate that double-checking introduces effective certainty > to the result, enabling us to claim to have "proved" that > M13,466,917 is the 39th Mersenne prime. > > As I am currently doing a double check I am interested in how the > probability of an erroneous LL test varies as we go from the bottom > to the top of the range of exponents for a given FFT size. > > The probability at the top of the range is presumably such that > the cost > in time of an erroneous LL test balances the extra time needed for the > next FFT size, for which the chance of error is small. > > David Eddy > _________________________________________________________________ > Be one of the first to try Windows Live Mail. > http://ideas.live.com/programpage.aspx?versionId=5d21c51a-b161- > 4314-9b0e-4911fb2b2e6d > > > ------------------------------ > > _______________________________________________ > Prime mailing list > [email protected] > http://hogranch.com/mailman/listinfo/prime > > > End of Prime Digest, Vol 30, Issue 20 > ************************************* > _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
