20081016, 14:40  #1 
"Robert Gerbicz"
Oct 2005
Hungary
2×3×227 Posts 
Riesel and Sierp numbers bases <= 1024
I've done some search on the sierpinski side up to base=1024,
see: http://robert.gerbicz.googlepages.com/sierpinski.txt 
20081016, 21:54  #2 
"Robert Gerbicz"
Oct 2005
Hungary
2×3×227 Posts 
Better Riesel values, also up to base=1024:
http://robert.gerbicz.googlepages.com/riesel.txt Last fiddled with by R. Gerbicz on 20081016 at 21:54 
20091216, 13:21  #3 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AB_{16} Posts 
I've converted the conjectures to a spreadsheet format for easy sorting by conjecture size. Attached are the two files in .csv format. Maybe someone else will find them useful.

20091218, 10:23  #4  
May 2007
Kansas; USA
2·3·19·89 Posts 
Quote:
That brings up several interesting questions: Is Riesel base 280 the highest known conjecture? Is it the highest possible conjecture for any base? Do we know for sure that there is not a smaller conjecture with a period > 36 like what happened with base 3, which has a period of 144? Perhaps Mr. Gerbicz might have some answers for us there. A couple of interesting notes: (1) Despite the many huge conjectures, the median conjecture is k=208 on both sides. (2) The smallest odd conjecture is k=13. I realize that lower odd conjectures are possible but there doesn't happen to be any for bases <= 1024. Last fiddled with by gd_barnes on 20091218 at 10:24 

20091218, 11:08  #5  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
2×2,837 Posts 
Quote:
Code:
E:\OurDocuments\Mersenne\covering>covering 144 280 1 100000 513613045571842 Checking k*280^n1 sequence for exponent=144, bound for primes in the covering set=100000, bound for k is 513613045571842 Examining primes in the covering set: 281,26227,78401,78121,17,13,9133,51769,19,37,433,18313,73,97,38833,23761,61057 And their orders: 2,3,4,6,8,12,12,12,18,18,18,24,36,48,48,144,144 **************** Solution found **************** 482870640360662 **************** Solution found **************** 371284522956233 **************** Solution found **************** 253971311388192 E:\OurDocuments\Mersenne\covering>covering 72 280 1 100000 513613045571842 Checking k*280^n1 sequence for exponent=72, bound for primes in the covering set=100000, bound for k is 513613045571842 Examining primes in the covering set: 281,26227,78401,78121,17,13,9133,51769,19,37,433,18313,73 And their orders: 2,3,4,6,8,12,12,12,18,18,18,24,36 **************** Solution found **************** 513613045571841 is this a bug in the covering program? 

20091218, 11:18  #6  
May 2008
Wilmington, DE
17·167 Posts 
Quote:


20091218, 11:52  #7 
Jan 2009
Ireland
2·3·31 Posts 
i was just looking at riesel base 280 last night,and was thinking it would be a good idea to start some sort of effort on it.i might do so work on it at a later stage.

20091218, 12:15  #8 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
2·2,837 Posts 
144 produces
Code:
**************** Solution found **************** 482870640360662 **************** Solution found **************** 371284522956233 **************** Solution found **************** 253971311388192 Code:
**************** Solution found **************** 203047772514813 **************** Solution found **************** 179533651185182 **************** Solution found **************** 106286297574924 **************** Solution found **************** 41294807980463 **************** Solution found **************** 31741813281359 not finished yet Code:
**************** Solution found **************** 367930956102524 **************** Solution found **************** 12775672337441 looks like adding a factor of 5 into the exponent is helpful sometimes i would be half surprised if 12775672337441 turns out to be the lowest value Last fiddled with by henryzz on 20091218 at 12:31 Reason: still another for 288 
20091218, 13:27  #9  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:
Code:
S15: 91218919470156 S280: 82035074042274 R511: 40789000085994 R15: 36370321851498 R280: 12775672337441 Last fiddled with by MiniGeek on 20091218 at 13:28 

20091218, 13:35  #10 
"Robert Gerbicz"
Oct 2005
Hungary
2·3·227 Posts 
I think none of the posted riesel k values for base=280 is good. Or am I wrong?
k=513613045571842 is still good. For such large searches the program can print out bad values, the reason is that when bound_for_k*bound_for_primes is very large, say about 2^60 or so. Here the order of the primes in the covering set is also important, because for the original k value p=78121 is in the covering set, but the code has found this solution. The solution would be to rewrite this in gmp to eliminate all such limitations. (I don't have time for this). It wouldn't be bad to check all k values for bases<=1024 for both sides. I'm not sure if I've done this. ps. OK, checked this in gmp, there is no wrong k values in the two files. Last fiddled with by R. Gerbicz on 20091218 at 13:58 
20091218, 14:00  #11  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
2×2,837 Posts 
Quote:


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