20070106, 07:55  #23 
Apr 2003
2^{2}·193 Posts 
Change my reservation i will sieve all noted k for base 17 (riesel and sierpinski)
Lars 
20070106, 08:40  #24 
Jun 2003
Oxford, UK
77E_{16} Posts 
Base 6
Did a little work this afternoon of base 6. Using the covering set [7,43,37,31,13] repeating every 24n provides a Sierpinski number 243417.
I will try to do the Riesel later. Note that the alternative set [7,43,37,31,97] repeating every 24n could also provide a lower Sierpinski value. However 243417 is at 0.73% of the product of this set's cover primes, and there are only 24 values to check, if I was any good at statistics I could tell you what the probability is, but I am not!! Regards Robert Smith 
20070106, 08:53  #25 
Jun 2003
1,579 Posts 
Candidates for 10
804*10^n+1 1024*10^n+1 2157*10^n+1 2311*10^n+1 2607*10^n+1 2661*10^n+1 2683*10^n+1 3301*10^n+1 3312*10^n+1 3345*10^n+1 3981*10^n+1 4069*10^n+1 4863*10^n+1 5028*10^n+1 5125*10^n+1 5512*10^n+1 5556*10^n+1 5565*10^n+1 6172*10^n+1 6687*10^n+1 6841*10^n+1 7404*10^n+1 7459*10^n+1 7534*10^n+1 7666*10^n+1 7809*10^n+1 7866*10^n+1 8194*10^n+1 8425*10^n+1 8454*10^n+1 8667*10^n+1 8724*10^n+1 8889*10^n+1 8922*10^n+1 8953*10^n+1 9021*10^n+1 9043*10^n+1 9175*10^n+1 9351*10^n+1 1343*10^n1 1506*10^n1 1803*10^n1 1935*10^n1 2111*10^n1 2276*10^n1 2333*10^n1 3015*10^n1 3332*10^n1 3356*10^n1 4016*10^n1 4421*10^n1 4478*10^n1 4577*10^n1 5499*10^n1 5897*10^n1 6588*10^n1 6633*10^n1 6665*10^n1 7019*10^n1 7602*10^n1 8174*10^n1 8579*10^n1 9461*10^n1 9701*10^n1 9824*10^n1 10176*10^n1 candidates for 16 riesel (upto 10,000) 450*16^n1 1343*16^n1 1803*16^n1 1935*16^n1 2333*16^n1 3015*16^n1 3332*16^n1 4478*16^n1 4500*16^n1 4577*16^n1 5499*16^n1 5897*16^n1 6588*16^n1 6633*16^n1 6665*16^n1 7019*16^n1 7602*16^n1 8174*16^n1 8579*16^n1 
20070106, 11:34  #26 
Jun 2003
Oxford, UK
2·7·137 Posts 
Riesel candidate for base 6
After a bit of fiddling about with [7,43,37,31,13] came up with the riesel candidate 213410 for base 6. 133946 is trivial.
Regards Robert Smith 
20070106, 12:07  #27 
Jun 2003
Oxford, UK
2×7×137 Posts 
Simple to prove
Sierpinskis and Riesels for the following bases are simple to find and should be relatively simple to prove as they have 2 prime factors in b^21 which are not in b1, and therefore have cover from these new prime factors, every 2n.
14 was the first such case, proven with S4, R4 20 is next with S8, R8, both proven The others exhibiting this small covering set, less than base =100, and which therefore should be relatively simple to prove are 29, 32, 34, 38, 41, 44, 50, 54, 56, 59, 62, 64, 65, 68, 69, 74, 76, 77, 83, 84, 86, 89, 90, 92, 94, 98 Someone might want to just run these quickly to prove them. Then we might bash on to find Sierpinskis and Riesels for all other bases up to 100. Tomorrow I start work again so time I can spend on this will be limited. Regards Robert Smith 
20070106, 12:49  #28 
"Mark"
Apr 2003
Between here and the
2^{2}×23×67 Posts 
I agree with that. My method works well if the Riesel/Sierpinski number is relatively small. Once you hit numbers that large it could take weeks, months, or even years to find one.

20070106, 14:14  #29  
Jun 2003
Oxford, UK
2·7·137 Posts 
Alternative approach
Quote:
So an approach would be to define, in principle, what properties covering sets must have. For example it is highly unlikely that a covering set would have no P which has a mulitplicative order in base b of less than 5. But can we prove this is the case? If we can, then we can say for certain that the covering set must have at least one of the prime factors of b^21, b^31 or b^41. Then we should be able to sieve out some k from providing a covering set, and only test those which meet the mod criteria. Just a few musings on an approach. Regards Robert Smith 

20070106, 17:03  #30 
Apr 2003
772_{10} Posts 
First one down:
88*17^4868+1 is prime. Lars Edit: Next one down: 44*17^64881 is prime. Riesel side done. Last fiddled with by ltd on 20070106 at 17:32 
20070106, 18:16  #31  
Sep 2006
BB_{16} Posts 
Think, I will try base 18
Quote:


20070106, 23:31  #32 
Jun 2003
1579_{10} Posts 
For base 16, I found a covering set [17,13,7,241] So S/R must be less than 372827
For base 32 [3,7,13,17,241] Last fiddled with by Citrix on 20070106 at 23:32 
20070106, 23:54  #33 
"Mark"
Apr 2003
Between here and the
2^{2}·23·67 Posts 
I think that it would make sense to either put up a website or make a sticky thread with the current status for each base. It is beginning to be difficult to follow this thread.

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