Re: Mersenne: Unable to communicate with server.
Where can we download version 22.4? The webpage at http://www.mersenne.org/freesoft.htm shows only version 21.4, from 22 Sep 2001 (for Windows). Thanks --Andy --On Wednesday, August 28, 2002 8:56 PM -0700 "Terry S. Arnold" <[EMAIL PROTECTED]> wrote: > All > > I just encountered the error 29 problem on several machines. All of them > were running 21.4. Two more machines that were running 22.4 were just > fine. I upgraded everybody to 22.8 and everything went back to normal in > terms of accessing the server. BTW during this time I could not ping > www.entropia.com. It looks like we all need to go to 22.8. For some > reason it copes with some sort anomaly that earlier version do not handle. > > Terry _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Prime Wiki
All, It seems I was too hasty. I have had a number of technical difficulties to do with DNS and apache (my fault of course) and the site was not working for a significant amount of time from my announcement. I wonder if people could let me know if it is all working. The url is now http://primes.hedges.net/ . Andy -Original Message- From: Andy Hedges [mailto:[EMAIL PROTECTED]] Sent: 17 July 2001 11:29 To: '[EMAIL PROTECTED]' Subject: Mersenne: Prime Wiki All, I have set up a Wiki to discuss Primes. It can be found at http://www.hedges.net/ . For those of you who don't know what a wiki it is a freely editable website. Go and try it for yourself to see. Andy ~~ ~~ Andy Hedges Consultant Proteus the Internet Consultancy Tel: + 44 (0)20 7566 7666 Fax: + 44 (0)20 7566 7677 Direct: + 44 (0)20 7566 7541 Web: http://www.proteus.co.uk Email: [EMAIL PROTECTED] Unit A, City Pavilion, 33 Britton St, London EC1M 5UG A Division of Proteus Ventures Ltd Registered in England: 3169362 VAT: 675007732 ~~ ~~ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Prime Wiki
All, I have set up a Wiki to discuss Primes. It can be found at http://www.hedges.net/ . For those of you who don't know what a wiki it is a freely editable website. Go and try it for yourself to see. Andy ~~ ~~ Andy Hedges Consultant Proteus the Internet Consultancy Tel: + 44 (0)20 7566 7666 Fax: + 44 (0)20 7566 7677 Direct: + 44 (0)20 7566 7541 Web: http://www.proteus.co.uk Email: [EMAIL PROTECTED] Unit A, City Pavilion, 33 Britton St, London EC1M 5UG A Division of Proteus Ventures Ltd Registered in England: 3169362 VAT: 675007732 ~~ ~~ _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Proth observations
Anyone have any idea why for k = 659 there are very little primes? In fact for k up to 20 there are none (I haven't found any in this range yet!). Andy -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] Sent: 23 June 2001 02:17 To: Gordon Bower; [EMAIL PROTECTED] Subject: Re: Mersenne: Proth observations Gordon Bower <[EMAIL PROTECTED]> observes > After seeing a post on this list a few weeks ago I decided to branch out > and try a few ranges from Michael Hartley's page looking for k*2^n-1 > primes. I must say there is a bit of a thrill in actually discovering a > new prime every day I run the program instead of proving two numbers a > month composite. :) > I assumed that one value of k was pretty much the same as any other as far > as execution time and the chance of finding primes. To my surprise this > turned out not to be so: On the P3-500, for "most" 650 about 5 hours for 16000 k=701 it took less than 2 and just over 6 hours, respectively. The > phenomenon is reproducible, doesn't seem to be an artifact of other > programs or reboots or suchlike. Any number theorists care to explain what > is special about k=701 that makes it easy to check for primality? > Fix k = 701. We check that If n == 1 (mod 2) then k*2^n == 1 (mod 3) If n == 0 (mod 4) then k*2^n == 1 (mod 5) If n == 6 (mod 8) then k*2^n == 1 (mod 17) If n == 0 (mod 3) then k*2^n == 1 (mod 7) Therefore k*2^n - 1 can be prime only if n == 2 or 10 (mod 24). We can eliminate more potential values of n using If n == 8 (mod 18) then k*2^n == 1 (mod 19) If n == 18 (mod 20) then k*2^n == 1 (mod 41) If n == 6 (mod 28) then k*2^n == 1 (mod 29) Some congruences are redundant; for example If n == 6 (mod 12) then k*2^n == 1 (mod 13) eliminates nothing new. k = 701 has less such redundancy than the typical k. _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Proth observations
Are all primes of this form probable primes of this form? Andy -Original Message- From: Hoogendoorn, Sander [mailto:[EMAIL PROTECTED]] Sent: 23 June 2001 10:02 To: '[EMAIL PROTECTED]' Subject: RE: Mersenne: Proth observations Brian J. Beesley Wrote: > My strategy is: > (1) run Proth at medium priority in factoring only mode to eliminate > candidates with "small" factors; For step 1 i use Newpgen. I think this is better configurable then proth in how far or long you want to factor. Don't know which is the fastest of the two. > (2) on the same system, run PRP at low priority to check the > survivors from stage 1 for probable primes; > (3) on a different system (normally running Prime95), run Proth at > medium priority to verify the probable primes. (If you don't have a > "spare" system it would be best to do this in a seperate directory so > as to save keep changing the Proth setup!) > BTW so far _every_ probable prime I've found using PRP has been > accepted as a genuine prime by Proth, though this is certainly not > guaranteed. Same here > If you break the run down as above you will see that some values of k > yield a much smaller proportion of candidates for psuedo-prime > testing than others. Or, to put it another way, some values of k give > a much higher percentage of k.2^p-1 with "small" factors than others. For some k's you have to test more the twice as many candidates in the same range of n's Sander _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: [slightly OT] Web discussion about distributed computing
>1775*2^332181+1 is prime! (10 digits) Discovered 22-Apr-2001 How was is found? _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: VB primality test program
The code is a terrible mess and hardly OO. If anyone makes any radical improvements to it I would love a copy. The URL is http://www.a0a.co.uk/mirrors/mersenne/LL.zip Andy -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Monte Westlund Sent: 13 March 2001 14:30 To: [EMAIL PROTECTED] Subject: Re: Mersenne: VB primality test program On Mon, 12 Mar 2001 22:12:54 -0800, you wrote: > >I'm afraid VB would be awfully slow at any sort of intensive numerical work >like this, and not very good with precision either, so I rather doubt anyone >has spent any signficant time on anything much more sophisticated than a >erathonese sieve program > >-jrp > I know VB would not be the first choice. It's more for benchmarking some machines(Prime95 is not an option on them), and to explore a bit. Monte _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: VB primality test program
I chucked together a LL agorithm in Java a while back in order to benchmark some JVM's. If anyone is interested I could post the source and bytecode to my website. btw :- It is many many times slower than Prime95 (as expected). Andy > -Original Message- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED]]On Behalf Of John R > Pierce > Sent: 13 March 2001 6:13 am > To: Monte Westlund; [EMAIL PROTECTED] > Subject: Re: Mersenne: VB primality test program > > > > I'm looking for a primality test program source code written in VB, > > for fun and adventure. Just want to mess around a little. Searched a > > little with no luck. > > I'm afraid VB would be awfully slow at any sort of intensive > numerical work > like this, and not very good with precision either, so I > rather doubt anyone > has spent any signficant time on anything much more > sophisticated than a > erathonese sieve program > > -jrp > > > __ > ___ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers > > _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
FW: Mersenne: bug in Wordpad?
Henk Stokhorst, It is not really the OS (although UNIX does have a lot of nice tools for this type of thing) it is wordpad that is not really the most capable text editor. If you are using Windows I would suggest you try TextPad which is available for 30 day evaluation from www.textpad.com. Hope this helps, Andy ~~ ~~ Andy Hedges Consultant Proteus the Internet Consultancy Tel: + 44 (0)207 689 Fax: + 44 (0)207 689 6667 Direct: + 44 (0)207 689 6669 Web: http://www.proteus.co.uk Email: [EMAIL PROTECTED] 26 Britton St, London EC1M 5UB A Division of Proteus Ventures Ltd Registered in England: 3169362 VAT: 675007732 ~~ ~~ -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Henk Stokhorst Sent: 30 October 2000 10:20 To: [EMAIL PROTECTED] Subject: Mersenne: bug in Wordpad? L.S., Whenever I have a large file (about 3.000 lines) with exponents to test (extracted from the nofactor.cmp file) and replace all the 'Test=' with 'Factor=' using wordpad (part of windows accesoires) one line gets to read 'Factorst='. Can other people reproduce this result? What OS would you recommend for such operations ;-) YotN, Henk Stokhorst _ 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
RE: Mersenne: GIMPSers in the news
I believe the cracking project is http://www.distributed.net/ ~~ ~~ Andy Hedges Consultant Proteus the Internet Consultancy Tel: + 44 (0)207 689 Fax: + 44 (0)207 689 6667 Direct: + 44 (0)207 689 6669 Web: http://www.proteus.co.uk Email: [EMAIL PROTECTED] 26 Britton St, London EC1M 5UB A Division of Proteus Ventures Ltd Registered in England: 3169362 VAT: 675007732 ~~ ~~ -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of [EMAIL PROTECTED] Sent: Thursday, October 12, 2000 5:57 PM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Mersenne: GIMPSers in the news Check out: http://www.cnn.com/2000/TECH/computing/10/12/britain.code.reut/index.html Of course, for me to claim Paul Leyland and Torbjorn Granlund as GIMPSers is a bit like the flea saying it owns the dog, but both have had (direct or indirect) involvement with the project in the past. Does anyone know the URL of the cracking project website mentioned in the above article? (There was no link to it from the CNN page.) -Ernst _ 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
Mersenne: Tips on compiling source
I'm trying to compile the source code for Prime95 for a wintel machine and am slightly lost for how to do so. I have Visual C++, gcc, a86 and just about everything else. My background is Java development (3 1/2 years) so I am not used to header files and assembly language. Though do know the fundamentals. Any help would be great. Also any programming tutorials etc (online or hard copy) on assembler would be great. Andy _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
Mersenne: Assignment of Exponents
Just a quick question. Are the lowest exponents assigned first or is it dependent on your CPU power or what? _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
RE: Mersenne: Error 11: exponent already tested!?!
Another enhancement would be to add the functionality to force a checkin with the server. Currently I have found the only way to do this is to alter the number of hours per day field. This is fairly minor compared to the problem of duplicated effort mentioned below but may elevate the problem slightly. Cheers Andy -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On Behalf Of Mikus Grinbergs Sent: Thursday, July 20, 2000 1:14 PM To: [EMAIL PROTECTED] Subject: Re: Mersenne: Error 11: exponent already tested!?! On 20 Jul 2000 00:09:20 -0400 "Robert Deininger" <[EMAIL PROTECTED]> wrote: > > I have saved some of the hourly status and cleared reports, and I think > I see what happened. > > On 13-May-2000: > 8277083 64 4126527 105.0 -12.1 42.9 > 16-Apr-00 19:40 29-Jan-00 22:24 floris Vincent > > This exponent was assigned to floris on 29-Jan-2000. > > On 25-Jun-2000: > 8277083 64 4126527 148.0 -55.1 -0.1 > 16-Apr-00 19:40 29-Jan-00 22:24 floris Vincent > > The exponent had just expired, but is still assigned to floris. I realize there are participants who will undergo "agonies similar to giving birth" unless ALL exponents through xxx are checked by such-and-such a date. Nevertheless, as the exponents being worked on start taking longer and longer on any given machine, could we PLEASE refocus GIMPS recordkeeping on the 'humane' aspect of the effort, rather than on the 'treadmill' aspect ? Because the GIMPS expiration limit has stayed at 60 days (rather than increasing with the exponents) I no longer try to run LL tests with my K6-III machine. [I run offline. If I am forced to "check in" by a given date even though I have not finished, for me it is simpler to just decline to participate.] The material I quoted from Robert Deininger appears to me to indicate that somebody who was working on an exponent failed to "check in" for at least 70 days. The exponent got assigned to a second person, who got upset when the original person suddenly completed his LL test. Wouldn't it be more 'humane' to wait a bit (i.e., to not 'expire' assignments after 70 days) ? Will the project truly suffer if "seemingly abandoned" exponents are NOT reassigned on a 'treadmill' schedule ? mikus _ 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
Mersenne: Record p-1 factors
Dear All, Firstly, apologies to anyone receiving multiple copies of this message. The following are the only six 30+ digit factors found by Pollard's p-1 of which I am aware: (1) p34=8222057557067636644603420882415653 p-1=2^2.3.17.23.43.11657.506797.1632809.1692107.2496721 N=917^43-1 By: Steward 1999 (2) p34=7146831801094929757704917464134401 p-1=2^8.5^2.11^2.23^2.821.3371.39209.3394739.47358559 N=575th Fibonacci Number By: Silverman 1989 (3) p33=451990098872812878233073602931247 p-1=2.3.7^2.29.1423.55457.1907071.5110913.68921857 N=782^49-1 By: Steward 1999 (4) p32=49858990580788843054012690078841 p-1=2^3.5.13.19.977.1231.4643.74941.1045397.11535449 N=2^977-1 By: Brent (5) p31=4302886402340485071334706663243 p-1=2.7^2.139.401.129757.183361.488893.67720951 N=303^49-1 By: Steward 1999 (6) p30=174463386657191516033932614401 p-1=2^8.5^2.17.37.1627.5387.68111.152081.477361 N=2^740+1 By: Baillie Please let me know of any others. I will allow a couple of weeks for replies and then collate them into an appendix to my website. As you will note from positions 1, 3 and 5 this is not entirely a detached or altruistic exercise! Regards, Andy _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Chance of P-1 factor
- Original Message - From: Alexander Kruppa <[EMAIL PROTECTED]> > I've been trying to figure out what the chance of finding a P-1 factor > is, given a certain amount of trial factoring and a P-1 bound. [...] > This would mean that we'd find factors of only 2.6% of the 10 million > exponents, even with a bound of 1M ! Thats pretty disappointing. To throw some experimental data in with the theory: I use p-1 with B1= 1e7 and B2 = 1e8 to try and factorize Generalized Repunits. The composites that I deal with range from say 75 to 150 digits so are much smaller than those Mersenne composites you are working on while having a similar restriction on the form of factors. The results: 8 successes in 1452 trials or 0.55% Andy Steward _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Odds on finding a factor ?
- Original Message - From: Lucas Wiman <[EMAIL PROTECTED]> > I think under windows that dos windows only run when they are "up". > (I could be wrong, I've stopped using windows again) No. You can set a background priority. In Win 95, right-click on the icon, then click "Properties". Click on the "Misc" tab and move the slider for "Idle Priority" anywhere you want between Low and High. Click "OK". If I'm going to be away from a machine for a while, I quite often set a "B" priority task running in a Ubasic window and minimise it, then run an "A" priority task running in an active window. That way, I ensure that the machine won't be idle if the "A" task completes before my return. The downside is the reduction in resources available to the "A" task while both are running. HTH, Andy Steward Factorisations of 57,619 Generalised Repunits at: <http://www.users.globalnet.co.uk/~aads/index.html> _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Re: Odd's on finding a factor (part 2)
Dave Mullin wrote: >Result = MODPOW(2,MersenneExponent,TrialFactor) >where TrialFactor is the MersenneExponent * 2 * (some k in range 1 to 2^16) + 1. >If Result = 1 then TrialFactor divides the Mersenne Prime. As UBASIC can >handle around 2600 >decimal digits, in theory (and with a lot of time), I >could check all factors up to 2600 decimal >digits for any given exponent. >It's a damn sight faster than filling 16MB+ of memory with 1's and >then trial dividing. Ubasic can indeed handle integers up to around 2600 digits, but modpow() needs to hold intermediate results, so will only work up to around 1300 digits input. Good luck anyway! Andy Steward _ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Lehmer question
Dear All, Following up my own msg here. First, there is an obvious linear relationship between my two conjectures, so they are equivalent. Second, predictions where possible (U=Unknown): p (p+1)/2 mod 31 Conj 1 (p-2) mod 31 Conj 2 4423 11 U 19 U 9689 9 - 15 - 9941 11 U 19 U 11213 27 U 20 U 19937 18 U 2 U 21701 1 U 30 U 23209 11 U 19 U 44497 22 U 10 U 86243 1 U 30 U 110503 10 - 17 - 132049 26 U 18 U 216091 11 U 19 U 756839 3 + 3 + 859433 26 U 18 U 1257787 28 - 22 - 1398269 23 - 12 - 2976221 18 U 2 U 3021377 28 - 22 - 6972593 6 U 9 U Regards, Andy Steward Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Re; Mersenne: Lehmer question
>Let Mp = 2^p - 1 be a Mersenne prime, where p > 2. >Denote S[1] = 4 and S[k+1] = S[k]^2 - 2 for k >= 1. >Then S[p-2] == +- 2^((p+1)/2) mod Mp. >Predict which congruence occurs. Dear Peter and All, This is as far as I can go in Ubasic: p Result 3 + 5 + 7 - 13 + 17 - 19 - 31 + 61 + 89 - 107 - 127 + 521 - 607 - 1279 - 2203 + 2281 - 3217 - 4253 + The algebra suggests two values to consider 1) Consider q=((p+1)/2) mod n Taking the p pairwise where signs differ eliminates the following possible n: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27, 28,29,30,32,33,34,35,36,37,38,39,40,42,43,45,46,47,48,49,51,52,54,55,57, 58,59,60,61,63,64,66,67,72,73,74,75,77,78,80,81,84,86,87,89,91,96,99,103, 104,111,114,115,120,122,125,126,127,129,131,133,144,146,151,154,156,162, 169,177,178,182,183,185,189,192,193,197,203,208,211,222,225,230,231,240, 245,254,258,259,262,263,266,267,273,288,297,301,302,309,311,312,319,347, 353,359,364,366,370,375,378,399,462,493,507,515,518,524,526,531,534,546, 549,555,567,569,576,609,622,624,633,637,638,691,694,706,789,798,801,803, 841,933,986,1041,1048,1057,1059,1077,1092,1093,1098,1110,1125,1134,1138, 1139,1487,1545,1578,1593,1602,1606,1607,1823,1866,2073,2082,2117,2118, 2123 That first gap at 31 is interesting... Conjecture: take ((p+1)/2) mod 31 if in (0,2,3,7,16,17,19) then sign(S[p-2]) = + if in (4,9,10,13,14,20,23,25,28) then sign(S[p-2]) = - if in (1,5,6,8,11,12,15,18,21,22,24,26,27,29,30,31) then no data 2) Consider q=(p-2) mod n Taking the p pairwise where signs differ eliminates the following possible n: 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27, 28,29,30,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,54, 55,56,57,58,59,60,61,63,64,66,67,68,70,72,73,74,75,76,77,78,80,81,84,86, 87,89,90,91,92,94,96,98,99,102,103,104,108,110,111,114,115,116,118,120, 122,125,126,127,128,129,131,132,133,134,144,146,148,150,151,154,156,160, 162,168,169,172,174,177,178,182,183,185,189,192,193,197,198,203,206,208, 211,222,225,228,230,231,240,244,245,250,252,254,258,259,262,263,266,267, 273,288,292,297,301,302,308,309,311,312,319,324,338,347,353,354,356,359, 364,366,370,375,378,384,386,394,399,406,416,422,444,450,460,462,480,490, 493,507,508,515,516,518,524,526,531,532,534,546,549,555,567,569,576,594, 602,604,609,618,622,624,633,637,638,691,694,706,718,728,732,740,750,756, 789,798,801,803,841,924,933,986,1014,1030,1036,1041,1048,1052,1057,1059, 1062,1068,1077,1092,1093,1098,1110,1125,1134,1138,1139,1152,1218,1244, 1248,1266,1274,1276,1382,1388,1412,1487,1545,1578,1593,1596,1602,1606, 1607,1682,1823,1866,1972,2073,2082,2096,2114,2117,2118,2123,2154,2184, 2186,2196,2220,2250,2268,2276,2278,2974,3090,3156,3186,3204,3212,3214, 3646,3732,4146,4164,4234,4236,4246 Again a gap at n=31 Conjecture: take (p-2) mod 31 if in (0,1,3,4,11,28,29) then sign(S[p-2]) = + if in (5,6,12,15,16,17,22,23,25) then sign(S[p-2]) = - if in (2,7,8,9,10,13,14,18,19,20,21,24,26,27,30,31) then no data It's all a bit thin and arm-waving, but I would be interested to see if a continuation of the series confirms or denies either of these conjectures. Regards, Andy Steward Factorisations of generalised repunits at: <http://www.users.globalnet.co.uk/~aads/index.html> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
