20200206, 09:34  #12 
"AMD YES!"
Jan 2020
Bellevue, WA
2^{3}×5 Posts 
Thank you so much!

20200206, 13:27  #13 
"AMD YES!"
Jan 2020
Bellevue, WA
101000_{2} Posts 
How to use covering.exe????
Now though, I'm stuck with a black window and anything I enter makes it close!

20200206, 14:02  #14  
"Dylan"
Mar 2017
2^{2}×3^{2}×13 Posts 
Quote:
1. exponent  Specifies a "period" in which a covering set could repeat. Typically 144 is a good value, but any small number with a lot of 2 and 3's as factors should work. 2. base  the base in k*b^n+/1 that you want a CK for. 3. Specifies whether you want to look for Riesel numbers (1) or Sierpinski numbers (1). 4. This number specifies the upper bound for primes used in the covering set. Only primes below this are considered when looking for a covering set. 5. This number specifies the largest k that will be considered when looking for a covering set. Here's an example, using Riesel Base 2, which has CK = 509203: Code:
C:\Users\Dylan\Desktop\prime finding\prime testing>covering 144 2 1 25000 1000000 Checking k*2^n1 sequence for exponent=144, bound for primes in the covering set=25000, bound for k is 1000000 Examining primes in the covering set: 3,7,5,17,73,13,257,19,241,37,109,97,673,433,577 And their orders: 2,3,4,8,9,12,16,18,24,36,36,48,48,72,144 **************** Solution found **************** 509203 

20200206, 15:38  #15 
"AMD YES!"
Jan 2020
Bellevue, WA
2^{3}·5 Posts 
When I enter no solution is found:
C:\Users\dlc04\OneDrive\桌面\PG\covering>covering 144 726 1 25000 1000000 Checking k*726^n1 sequence for exponent=144, bound for primes in the covering set=25000, bound for k is 1000000 Examining primes in the covering set: 727,601,877,7,97,137,19,13,37,15601,17,113,2593,73,433,1873,193,577,10369,13249 And their orders: 2,4,4,6,8,8,9,12,12,12,16,16,16,18,24,36,48,144,144,144 
20200206, 15:42  #16 
"AMD YES!"
Jan 2020
Bellevue, WA
2^{3}×5 Posts 
When I enter no solution is found:
Code:
C:\Users\dlc04\OneDrive\桌面\PG\covering>covering 144 726 1 25000 1000000 Checking k*726^n1 sequence for exponent=144, bound for primes in the covering set=25000, bound for k is 1000000 Examining primes in the covering set: 727,601,877,7,97,137,19,13,37,15601,17,113,2593,73,433,1873,193,577,10369,13249 And their orders: 2,4,4,6,8,8,9,12,12,12,16,16,16,18,24,36,48,144,144,144 
20200206, 15:45  #17 
"Curtis"
Feb 2005
Riverside, CA
1000001011100_{2} Posts 
So you've learned there is no solution below 1 million (at least, using the parameter 144).
The conjectured k is just over 12 million according to the NPLB site, so this "no solution" should not surprise you. 
20200206, 16:03  #18 
"AMD YES!"
Jan 2020
Bellevue, WA
28_{16} Posts 
Code:
Checking k*726^n+1 sequence for exponent=216, bound for primes in the covering set=25000, bound for k is 100000000 Examining primes in the covering set: 727,601,877,7,97,137,19,13,37,15601,73,433,19441,1873,109,541,1297,3457 And their orders: 2,4,4,6,8,8,9,12,12,12,18,24,27,36,108,108,108,216 **************** Solution found **************** 28053477 **************** Solution found **************** 10923176 
20200206, 16:58  #19  
Jul 2003
535_{16} Posts 
Quote:
The 10923176 result matches the conjectured k here. Last fiddled with by masser on 20200206 at 16:59 

20200207, 03:08  #20 
"AMD YES!"
Jan 2020
Bellevue, WA
2^{3}·5 Posts 
okie, thanks everyone for answering!

20200211, 03:51  #21  
Nov 2016
3·647 Posts 
Quote:
Like this problem (Sierpinski case: find and prove the smallest k such that (k*b^n+1)/gcd(k+1,b1) is not prime for all n>=1) (Riesel case: find and prove the smallest k such that (k*b^n1)/gcd(k1,b1) is not prime for all n>=1), I cannot find such k for b = 66 and b = 120 (for both sides (Sierpinski and Riesel)). Last fiddled with by sweety439 on 20200211 at 03:54 

20200327, 08:09  #22 
Romulan Interpreter
Jun 2011
Thailand
2^{2}·2,137 Posts 
Sorry for waking up this old thread, but I didn't want to create a new one, and the subject of the current one seems suitable for my silly question:
Why 81 was chosen as the conjectured k for Riesel base 1024? 
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