Mersenne Digest Thursday, September 21 2000 Volume 01 : Number 779 ---------------------------------------------------------------------- Date: Mon, 18 Sep 2000 21:16:52 +0200 From: "Martijn Kruithof" <[EMAIL PROTECTED]> Subject: Re: Mersenne: primenet assignment question Hi, If you want double-checks, you can indicate this in the setup, go to the test/primenet menu, here you can indicate the type of work you want to do, this overrides the cpu setting. I can see that your exponent was reserved 2,4 days ago and expires in 85,6 days. After 88 days your exponent expires, unless you contact the primenet server earlier. In your case prime95 will try to connect to the primenet server after 28 days, then extending the exponent(s) you are working on. You can also do this manually when connected to the internet. (You can even indicate you want some 100 days by sending vacation information). You do not have to finish the assignment within the 88 days. Your reservation has to be extended before the exp column hits 0, and you could theoretically keep this assignment forever. Please do not start to format your text using outlook, many people will not be able to read your mails anymore. (You can try to put under Tools / options / Read / Fonts both the proportional and fixed font to courier new (font size smaller). And you will see be able to format using fixed fonts (and see the formatting others apply using a fixed font). This way the message is still sent unformatted as plain text.) Kind Regards, Martijn - ----- Original Message ----- From: "george de fockert" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, September 18, 2000 7:46 PM Subject: Mersenne: primenet assignment question > Dear primers, > > My 533 celeron which I configured for 4 hours/day has been given the > following assignment (copied from status page and sorry for the formatting, > anybody knows how to install a fixed font for outlook ?). > > prime fact current days > exponent bits iteration run / to go / exp date updated date > assigned computer ID Mhz Ver > -------- -- ---- --------- ----------------- --------------- ---------- - -- > --- ------------ ---- --- > 5627753 D* 63 37.8 -5.0 55.0 26-Aug-00 17:52 11-Aug-00 > 23:02 C274E1CE1 533 v19/v20 > 10356833 64 2.4 59.6 85.6 16-Sep-00 > 07:37 C274E1CE1 533 v19/v20 > > Why ? > 533 * 4/24 is below 100MHz equivalent, so I expect doublechecks. > Are all exponents doublechecked ? > This assignment will keep it busy for more than half a year, so it will > expire ! > > Even 4 hours is probably a too high estimate for my 'prime' computer time, > because during scanning, all CPU time > goes to waiting for my scanner, I hate polling drivers ! > > George de Fockert > > _________________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt > _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Mon, 18 Sep 2000 18:41:50 -0700 From: "Osher Doctorow" <[EMAIL PROTECTED]> Subject: Mersenne: Will the real operation please stand up? From: Osher Doctorow, Ph.D. [EMAIL PROTECTED], Mon. Sept. 18, 2000, 6:06PM In attempting to find a shorter proof of Fermat's Last Theorem (FLT) than the current one, I have become interested in the rather curious expressions g(x,y) = 1 - x + y and f(x,y) = x + y - xy. I have elsewhere indicated how an n-dimensional generalization of the real conjugate of one or both of these expressions would lead to a super-short proof of FLT - the real conjugate of g(x.y) is defined as 1 + x - y and the real conjugate of f(x,y) is defined as x + y -xy. Abstracts of 46 of my over 100 papers can be found on the internet at the Institute for Logic of the University of Vienna, http://www.logic.univie.ac.at, select ABSTRACT and then BY AUTHOR and then my name. However, I am here presenting a slightly different problem which is indirectly linked to Mersenne Primes via the Sophie Germain Prime - FLT - Fermat Number - Mersenne Number linkage. To shorten the presentation, I became curious about the expression (x - y)^^2 = x^^2 - 2xy + y^^2 and how it relates to f(x,y) = x + y - xy. Is it possible that either f(x,y) or f1(x,y) = x + y - 2xy is actually representable as a power of x - y? The answer seems to be no in the ordinary sense of power or exponent, but what about ordinals, cardinals, etc.? Is it possible that below the second power, there is a different infinite continuum of exponents from the familiar one? If so, then 2 would be the boundary between two continua, and this might explain its importance in FLT itself. Setting f(x,y) = xy yields x + y = 2xy or x + y - 2xy = 0, or f1(x,y) = 0. Anticipating things, let us write "a" as the exponent of x-y involved in f1(x,y), so (x-y)^^a = 0 is equivalent to f1(x,y) = 0. However, I have shown elsewhere that xy is a "different animal" from x or y not just in the sense of a polynomial but in a sense analogous to the quaternion/octonion multiplication of vectors/pseudovectors u and v, which is written uv. Thus, f(x,y) = xy has interest in itself as a sort of extreme/semi-extreme case, which means that (x-y)^^a is of interest in itself. We also have the equations x + y + xy = xy, which is equivalent to x + y = 0, and x + y + xy = -xy, which says that x + 2xy + y = 0, which seems to give rise to (x+y)^^a, and x - y - 2xy = -2xy which says x - y = 0. Notice that x - y - 2xy is obtained from x + y + 2xy by replacing y by -y. Finally, the perfect numbers are sums of their smaller divisors (among integers), which means that xy/x + xy/y + other expressions equal the perfect number xy if xy is the product x times y. Also, any even perfect number has form 2^^(r-1)(2^^r - 2) if 2^^r and r are prime, from Euclid's Elements. As far as I know, no odd perfect number exists. Thus, some sort of xy factorization could be conjectured for all perfects (or at least for very many). The Mersenne primes have form 2^^r - 2 for r prime, of course. I hope to continue this soon. Osher Doctorow _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Mon, 18 Sep 2000 19:23:26 -0700 From: "Osher Doctorow" <[EMAIL PROTECTED]> Subject: Mersenne: Will the real operation please stand up? From: Osher Doctorow, Ph.D. [EMAIL PROTECTED], Mon. Sept. 18, 2000, 7:32PM The expression "the real conjugate of f(x,y) is defined as x + y - xy" should read x + y + xy instead of x + y - xy. This was a typographical error. Osher Doctorow _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Tue, 19 Sep 2000 17:18:08 +0800 From: "Dave Mullen" <[EMAIL PROTECTED]> Subject: Mersenne: Will the real Mersenne formula please stand up? This is a multi-part message in MIME format. - ------=_NextPart_000_0020_01C0225D.94832720 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Osher Doctorow, I was following you right up until the last paragraph, where you seem to = have some misinformation on Perfect Numbers and Mersenne Primes. ... Also, any even perfect number has form 2^^(r-1)(2^^r - 2) ... Nope, perfect numbers have the form 2^^(r - 1)(2^^r - 1), examples :- where r =3D 2 ---> 2^^(1)(2^^2-1) =3D 2 x 3 =3D 6 where r =3D 3 ---> 2^^(2)(2^^3-1) =3D 4 x 7 =3D 28 where r =3D 5 ---> 2^^(4)(2^^5-1) =3D 16 x 31 =3D 496 A Perfect Number can only be made (as far as I know) by taking a = Mersenne Prime, and multiplying it by 2 to the power of the Prime = Exponent minus 1. So M(5) =3D 31, P(5) =3D 31 * (2^^4).=20 This is unless someone manages to find an odd perfect number (which = personally I doubt exists). ... if 2^^r and r are prime ... ? Erm, regardless whether r is prime or composite, 2^^r is always = composite (2x2x2x........x2) ! ... The Mersenne primes have form 2^^r - 2 for r prime, of course ... Of course not, Mersenne primes have form 2^^r - 1 ! Regards Dave - ------=_NextPart_000_0020_01C0225D.94832720 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content=3D"text/html; charset=3Diso-8859-1" = http-equiv=3DContent-Type> <META content=3D"MSHTML 5.00.2614.3500" name=3DGENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=3D#ffffff> <DIV><FONT face=3DArial size=3D2>Osher Doctorow,</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>I was following you right up until the = last=20 paragraph, where you seem to have some misinformation on Perfect Numbers = and=20 Mersenne Primes.</FONT></DIV> <DIV> </DIV> <DIV><FONT face=3DArial size=3D2>... Also, any even perfect number has = form=20 2^^(r-1)(2^^r - 2) ...</FONT></DIV> <DIV> </DIV> <DIV><FONT face=3DArial size=3D2>Nope, perfect numbers have the form = 2^^(r - 1)(2^^r=20 - - 1), examples :-</FONT></DIV> <DIV> </DIV> <DIV><FONT face=3DArial size=3D2>where r =3D 2 ---> 2^^(1)(2^^2-1) = =3D 2 x 3 =3D=20 6</FONT></DIV> <DIV><FONT face=3DArial size=3D2>where r =3D 3 ---> 2^^(2)(2^^3-1) = =3D 4 x 7 =3D=20 28</FONT></DIV> <DIV><FONT face=3DArial size=3D2>where r =3D 5 ---> 2^^(4)(2^^5-1) = =3D 16 x 31=20 =3D 496</FONT></DIV> <DIV> </DIV> <DIV><FONT face=3DArial size=3D2>A Perfect Number can only be made (as = far as I=20 know) by taking a Mersenne Prime, and multiplying it by 2 to the = power of=20 the Prime Exponent minus 1. So M(5) =3D 31, P(5) =3D 31 * (2^^4). = </FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>This is unless someone manages to find = an odd=20 perfect number (which personally I doubt exists).</FONT></DIV> <DIV> </DIV> <DIV><FONT face=3DArial size=3D2>... if 2^^r and r are prime ... = ?</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>Erm, regardless whether r is prime or = composite,=20 2^^r is always composite (2x2x2x........x2) !</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>... The Mersenne primes have form 2^^r = - - 2 for r=20 prime, of course ...</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>Of course not, Mersenne primes have = form 2^^r - 1=20 !</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>Regards</FONT></DIV> <DIV><FONT face=3DArial size=3D2></FONT> </DIV> <DIV><FONT face=3DArial size=3D2>Dave<BR></DIV></FONT></BODY></HTML> - ------=_NextPart_000_0020_01C0225D.94832720-- _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Tue, 19 Sep 2000 15:12:02 -0500 From: [EMAIL PROTECTED] Subject: Mersenne: FFT "If you are not well founded in the calculus there is precious little available in the literature."(Quote from the book UNDERSTANDING THE FFT by Anders E. Zonst) I totallt agree. I bought this book because it states on the cover "A tutorial on the algorithm & Software for Laymen, Students, Technicians & Working Engineers" Well, I am a laymen and I still can't follow this book. I haven't even been able to understand even one complete chapter. What ever happened to the teachers? I have always believed that if a person really knows a subject, he can teach it. He just goes step by step, giving examples (in real number calculations, not greek and latin). Can anyone help me find a true tutorial, book, or guide to the FFT? I have looked at about 15 different Web pages on the topic and the only book I have seen, on the net, that might present FFT's in a way that a layman could learn from is priced at about $80.00. And from what I have seen and experienced I wouldn't bet on this book either. I am a good student when I set my mind on a subject. Thanks Dan _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Thu, 21 Sep 2000 12:01:45 -0400 From: Pierre Abbat <[EMAIL PROTECTED]> Subject: Mersenne: NFSNET Anyone know what happened to Conrad Curry? His page has been saying for months that 2,679- is 40% sieved, but when I tried to get another range to sieve, the script appears to have run out of ranges. phma _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ End of Mersenne Digest V1 #779 ******************************
