20080525, 12:18  #56  
Jun 2003
Oxford, UK
753_{16} Posts 
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20080525, 13:13  #57  
Jan 2005
111011111_{2} Posts 
Quote:
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20080525, 16:03  #58 
"Robert Gerbicz"
Oct 2005
Hungary
575_{16} Posts 
Again, new record for Sierpinski, base=3:
1125458784774*3^n+1 is composite for all n values. Covering set=5,7,13,17,19,37,41,73,193,757 
20080525, 18:59  #59  
Quasi Admin Thing
May 2005
13×71 Posts 
Quote:
Now I'm just wondering, is there someway to make this a distributed effort, in order to find more covering sets or can the tast of finding covering sets only be at one machine at a time? Also how do you start this search, from lowest k and up or from conjectured k and then goes down? Regards Kenneth! 

20080525, 21:17  #60  
"Robert Gerbicz"
Oct 2005
Hungary
11×127 Posts 
Quote:
125050976086*3^n+1 is composite for all n. covering set=5,7,13,17,19,37,41,193,757 Small correction: For the above posted Sierpinski base=7 record k=1112646039348 this is a smaller covering set: 5,13,19,43,73,181,193,1201 Now you can also enjoy the search! (I've stopped it.) I've uploaded my code, you can download it: http://robert.gerbicz.googlepages.com/covering.c And an exe optimized by flags for P4: http://robert.gerbicz.googlepages.com/covering.exe The program requires 5 integers to start: exponent base C primebound best where we are testing exponent, it means that the period of the covering set's length will be this number (or it's divisor), known good examples are those where this number has got lots of small divisors, say exponent=24,72,144,... base is the base of the sequence C is 1 for Sierpinski, 1 for Riesel, it means we are testing k*b^n+C sequence (it isn't interesting, but you can use other values also) primebound: up to this number we consider all primes which divides b^exponent1, I've used 10000, you can use larger/smaller values for it, but very large, say 1000000 is obviously inefficient and slow down the program best: upper bound for the k value, we are searching k values for that k<best. It's good to set it to the best knwon k+1. Note that the product of the last two parameters should be < 2^62, otherwise it'll be an integer overflow. (For our search it isn't very interesting.) I think up to base<2^15 the program is good. Here are some examples to (re)discover currently known record solutions: 24 15 1 10000 100000000000000 find in 1 second k=91218919470156 for exponent=24, base=15, 1 so Sierpinski, prime bound=10000, best k=100000000000000 24 7 1 10000 2000000000000 find in 1 second k=1112646039348 for exponent=24, base=7, 1 so Sierpinski, prime bound=10000, best k=2000000000000 144 3 1 10000 126000000000 find (this took about half an hour or so) k=125050976086 for exponent=144, base=3, 1 so Sierpinski, prime bound=10000, best k=126000000000 24 7 1 10000 410000000000 find in 1 second k=408034255082 for exponent=24, base=7, 1 so Riesel, prime bound=10000, best k=410000000000 

20080526, 12:07  #61 
Jun 2003
Oxford, UK
3×5^{4} Posts 
Robert
I am so happy you have posted a windows executable! I am planning to research base 3 some more. Do you have any timings for your programme when you get into larger "exponents" such as 330 or 2310, as 3^111 brings in two smallish primes, 23 and 3851? 
20080526, 12:30  #62 
"Robert Gerbicz"
Oct 2005
Hungary
11×127 Posts 
It's hard to predict the timing. I would try only those exponents, which are divisible by 24, all recently found record solutions have period length divisible by 24! So 330,2310 aren't a very good run. Yes, they bring in 23, but lots of small primes are excluded from the covering set, see the listed primes if you run the program.
Last fiddled with by R. Gerbicz on 20080526 at 12:35 
20080526, 13:07  #63  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2×2,861 Posts 
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20080526, 13:58  #64  
Jun 2003
Oxford, UK
3×5^{4} Posts 
Quote:
I am nervous because CRM does provide unpredictable results, and it is possible that, with the mods all lining up, a quite low value might pop out as a solution, despite the superficially unattractive modulo order of the candidate cover set primes and mod requirements for each prime. 

20080526, 14:40  #65  
"Robert Gerbicz"
Oct 2005
Hungary
11×127 Posts 
Quote:
Last fiddled with by R. Gerbicz on 20080526 at 14:42 

20080526, 17:09  #66  
Oct 2006
259_{10} Posts 
i'm testing sierp base 3 ... first results:
Quote:
Last fiddled with by tnerual on 20080526 at 17:45 Reason: better solution again 

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