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Old 2020-02-06, 09:34   #12
dannyridel
 
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Thank you so much!
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Old 2020-02-06, 13:27   #13
dannyridel
 
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Thumbs down How to use covering.exe????

Now though, I'm stuck with a black window and anything I enter makes it close!
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Old 2020-02-06, 14:02   #14
Dylan14
 
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Quote:
Originally Posted by dannyridel View Post
Now though, I'm stuck with a black window and anything I enter makes it close!
Once you run covering.exe, it will expect 5 numbers. The meaning of those numbers is shown below:

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^n-1 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
Between each of those numbers you have to press enter.
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Old 2020-02-06, 15:38   #15
dannyridel
 
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When I enter no solution is found:
C:\Users\dlc04\OneDrive\桌面\PG\covering>covering
144
726
-1
25000
1000000
Checking k*726^n-1 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
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Old 2020-02-06, 15:42   #16
dannyridel
 
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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^n-1 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
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Old 2020-02-06, 15:45   #17
VBCurtis
 
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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.
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Old 2020-02-06, 16:03   #18
dannyridel
 
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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
???
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Old 2020-02-06, 16:58   #19
masser
 
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Quote:
Originally Posted by dannyridel View Post
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
???
I don't recall ever using this program, but it appears to have found two solutions (k values with covering sets). A typical Sierpinski conjecture will be that the smallest k value with a covering set is the smallest k for which the given sequence has no primes. A proof follows by finding a prime for each k less than 10923176.

The 10923176 result matches the conjectured k here.

Last fiddled with by masser on 2020-02-06 at 16:59
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Old 2020-02-07, 03:08   #20
dannyridel
 
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okie, thanks everyone for answering!
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Old 2020-02-11, 03:51   #21
sweety439
 
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Quote:
Originally Posted by Dylan14 View Post
Once you run covering.exe, it will expect 5 numbers. The meaning of those numbers is shown below:

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^n-1 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
Between each of those numbers you have to press enter.
Can this problem be used for finding the smallest k (coprime to c) with covering set for the general case (k*b^n+c)/gcd(k+c,b-1)? For b>=2, c !=0, gcd(b,c)=1

Like this problem (Sierpinski case: find and prove the smallest k such that (k*b^n+1)/gcd(k+1,b-1) is not prime for all n>=1) (Riesel case: find and prove the smallest k such that (k*b^n-1)/gcd(k-1,b-1) is not prime for all n>=1), I cannot find such k for b = 66 and b = 120 (for both sides (Sierpinski and Riesel)).
Attached Files
File Type: txt Conjectured smallest Riesel number.txt (8.3 KB, 20 views)
File Type: txt Conjectured smallest Sierpinski number.txt (8.3 KB, 20 views)

Last fiddled with by sweety439 on 2020-02-11 at 03:54
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Old 2020-03-27, 08:09   #22
LaurV
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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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