Mersenne Digest Monday, September 18 2000 Volume 01 : Number 778 ---------------------------------------------------------------------- Date: Thu, 14 Sep 2000 11:27:30 -0700 (PDT) From: John R Pierce <[EMAIL PROTECTED]> Subject: Re: Mersenne: Why do I get only double-checks > > I'm using a P3-500E box at college to run mprime. > > The relevant lines of the local.ini look like > > LastEndDatesSent=967023734 > RollingStartTime=968950008 > RollingAverage=4000 > CPUType=1 > CPUSpeed=500 > CPUHours=24 > > How come I get given only double-checks to do? I don't mind too much -- the > machine kills off a double-check in ten days -- but I'd be slightly > surprised if the frontier of 'obsolete; use for double-checks only' had > reached this one-year-old box yet. That Rolling Average figure looks kind of > high, too. your rolling average of 4000 indicates your computer is 4 times slower than a 'typical' 500. Wierd tho, CPUType=1 ??!? s/b = 9 or 10 or something. - -jrp _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Fri, 15 Sep 2000 00:00:06 -0500 From: Ken Kriesel <[EMAIL PROTECTED]> Subject: Re: Mersenne: Why do I get only double-checks Setting CPU type in prime95 V20.4.1 and then examining local.ini, CPUType=3 is a Cyrix 6x86 CPUType=4 is a 486 CPUType=5 is a Pentium CPUType=6 is a Pentium Pro CPUType=7 is an AMD K6 CPUType=8 is a Celeron CPUType=9 is a PentiumII CPUType=10 is a PentiumIII CPUType=11 is an AMD Athlon So CPUType=1 must be what, an Intel 80286? (More likely an unsupported value.) If I enter CPUType=1 or 2 or 3, while editing local.ini, prime95 displays it as a Cyrix 6x86. RollingAverage=1000 means the system runs iterations at 1000/1000 the expected speed (indexed relative to George Woltman's PII-400 on a per-Megahertz basis) Lower RollingAverage numbers mean lower performance. Higher numbers, higher performance. Your P3-500 is performing much better than the lowly cpu type the program thinks it is. But it is given only double checks because the program thinks it's a much slower cpu type than it actually is, and so does the primenet server. Make the CPUType in local.ini match the actual processor type, and you can get first-time tests, and use code that's more efficient for your cpu because it's what George tuned for it. Options, CPU, click on Pentium III. Ken At 06:38 PM 9/14/2000 +0100, you wrote: >I'm using a P3-500E box at college to run mprime. > >The relevant lines of the local.ini look like > >LastEndDatesSent=967023734 >RollingStartTime=968950008 >RollingAverage=4000 >CPUType=1 >CPUSpeed=500 >CPUHours=24 > >How come I get given only double-checks to do? I don't mind too much -- the >machine kills off a double-check in ten days -- but I'd be slightly >surprised if the frontier of 'obsolete; use for double-checks only' had >reached this one-year-old box yet. That Rolling Average figure looks kind of >high, too. > >Tom > >_________________________________________________________________________ >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: Sat, 16 Sep 2000 03:40:49 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Re: A new series of Mersenne-like Gaussian primes On 07/09/2000 at 18:27:23 GMT [EMAIL PROTECTED] wrote: >Dear Mike and others, > This sequence is in actuality two sequences in one. The >first are primes of the form 2^n - 2^[(n+1)/2] +1 and the other are >primes of the form 2^n + 2^[(n+1)/2] +1, as you have delineated. >I direct you to the following URL which is the home of the Sloane's >On-Line Encyclopedia of Integer Sequences. >http://www.research.att.com/~njas/sequences/ > You will find the sequences as numbers A007670 & A007671. >Their addresses are: >http://www.research.att.com/cgi->bin/access.cgi/as/njas/sequences/eisA.cgi?An um=A007670 >http://www.research.att.com/cgi->bin/access.cgi/as/njas/sequences/eisA.cgi?An um=A007671 >Hope you make use of this vital resource. >Sincerely yours, >Robert G. "Bob" Wilson v >Ph.D. ATP / CF&GI While happily acknowledging that the first 25 of these 33 (so far known) primes figure in that excellent database, I strongly dispute your assertion that "this sequence is in actuality two sequences in one". Why do you want to split the single series s[n] = (1+i)^n - 1 depending on whether n = 1 or 7 mod 8 (i.e. s[n] is in the right half of the complex plane) or not? Aurifeuille pointed out in 1873 [cf. Knuth, Vol. 2, p. 376] the identity 2^(4*m+2) + 1 = (2^(2*m+1) + 2^(m+1) + 1) * (2^(2*m+1) - 2^(m+1) + 1) and to this day numbers of the form (2^(2*m+1) + 2^(m+1) + 1) and (2^(2*m+1) - 2^(m+1) + 1) seem to only figure in the literature as _factors_ of the supposedly more worthy-of-study Fermats (see Cunningham project, etc.). But this is to miss entirely the unitary nature of the Gaussian series of which they are the modulus. My argument is as follows. Why is M[n] = 2^n - 1 an interesting sequence? Consider M[b,n] = b^n-1, for b a rational integer. For all n >= 1, this has the factor (b-1). So M[b,n] is certainly composite (for n >= 2) unless this factor is trivial (i.e. a unit +1 or -1), which happens in just 2 cases:- b = 2, giving the Mersennes M[n]; b = 0, which is uninteresting. Now consider G[c,n] = c^n - 1, for c a complex (Gaussian) integer. For all n >= 1, this has the factor (c-1). So G[c,n] is certainly composite (for n >= 2) unless this factor is trivial (i.e. a unit +1, -1, +i or -i), which happens now in 4 cases:- c = 2, giving the Mersennes, M[n]; c = 0, which is uninteresing; c = 1+i, giving the new series we are talking about, s[n] = (1+i)^n - 1; c = 1-i, giving the complex conjugate of this series. One might now naturally be drawn to investigate H[c,n] = c^n - i, for complex c, but, remarkably, we get no new candidate primes, just some old friends again: For all n >= 1, H[c,n] has the factor (c-i), and so is composite (for n >= 2) unless this factor is trivial (i.e. a unit +1, -1, +i or -i), which happens in 4 cases:- c = 1+i, giving the series (1+i)^n - i, which encompasses all the Fermats except F0, plus those M[n] and s[n] with n = +1 mod 4; c = -1+i, giving the series (-1+i)^n - i, which yields all the Fermats except F0, plus those M[n] with n = -1 mod 4 and those s[n] with n = +1 mod 4; c = i+i, giving the series (2*i)^n - i, which covers all the Fermats except F0 & F1, plus those M[n] with n = +1 mod 4; c = 0, which is uninteresing. Are you not convinced that we have here just one (rather beautiful) new series? An appeal to all you guys out there with lots of CPU cycles: let's find the 34th, 35th... prime terms - there's no reason other than machine time why the 40th (e.g.) should not become the largest known prime. Send an email to [EMAIL PROTECTED] to receive a range of exponents to check out. Mike Oakes _________________________________________________________________________ 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 19:46:50 +0200 From: "george de fockert" <[EMAIL PROTECTED]> 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 ------------------------------ End of Mersenne Digest V1 #778 ******************************
