mersenneforum.org Conjectured K question
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 2020-02-06, 09:34 #12 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 23·5 Posts Thank you so much!
 2020-02-06, 13:27 #13 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 1010002 Posts How to use covering.exe???? Now though, I'm stuck with a black window and anything I enter makes it close!
2020-02-06, 14:02   #14
Dylan14

"Dylan"
Mar 2017

22·32·13 Posts

Quote:
 Originally Posted by dannyridel 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.

 2020-02-06, 15:38 #15 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 2816 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^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
 2020-02-06, 15:42 #16 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 4010 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^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
 2020-02-06, 15:45 #17 VBCurtis     "Curtis" Feb 2005 Riverside, CA 47×89 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.
 2020-02-06, 16:03 #18 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 23×5 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 ???
2020-02-06, 16:58   #19
masser

Jul 2003

2×5×7×19 Posts

Quote:
 Originally Posted by dannyridel 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

 2020-02-07, 03:08 #20 dannyridel   "AMD YES!" Jan 2020 Bellevue, WA 508 Posts okie, thanks everyone for answering!
2020-02-11, 03:51   #21
sweety439

Nov 2016

111100001102 Posts

Quote:
 Originally Posted by Dylan14 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
 Conjectured smallest Riesel number.txt (8.3 KB, 16 views) Conjectured smallest Sierpinski number.txt (8.3 KB, 15 views)

Last fiddled with by sweety439 on 2020-02-11 at 03:54

 2020-03-27, 08:09 #22 LaurV Romulan Interpreter     Jun 2011 Thailand 853610 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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