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 2010-12-23, 21:17 #1 gd_barnes     May 2007 Kansas; USA 101101001110102 Posts Bases > 1030 and k's > CK Use this thread for reporting reservations/statuses/primes for bases > 1030 or for k's > the conjectured k of bases <= 1030. Note that these efforts will be outside the scope of the project and will not be formally shown anywhere. Last fiddled with by gd_barnes on 2011-03-03 at 05:51 Reason: new thread
 2011-01-07, 04:29 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 97×103 Posts I have tested R1031, CK 44. 3k remain at n=25,000. I would like to reserve it to 50K. Code: :::pl_trivial.txt::: 6 16 26 36 :::pl_prime.txt::: 2*1031^1722-1 12*1031^22-1 18*1031^3-1 20*1031^2-1 24*1031^2-1 28*1031^1-1 30*1031^3-1 32*1031^42-1 34*1031^1-1 38*1031^10-1 42*1031^236-1 22*1031^2897-1 40*1031^4273-1 14*1031^16166-1 :::pl_remain.txt::: 4*1031^n-1 8*1031^n-1 10*1031^n-1
 2011-02-19, 18:45 #3 10metreh     Nov 2008 44228 Posts A little bit of fun Just for fun, I decided to see what the conjectured Riesel and Sierp ks for base 65535 would be. As bases 3 (4-1) and 15 (16-1 = 2^4-1) have very high conjectured ks, I reasoned that 65535 (2^16-1) might also have a high conjecture. And finding a Riesel or Sierp k at all was harder than one might think, as the conjectures (which may not be the lowest) and covering sets show: Riesel: Conjectured k: 929606540198368 Covering set: {13, 37, 61, 193, 877, 22253377} Period: 12 Sierp: Conjectured k: 10766873647286 Covering set: {13, 37, 61, 193, 1657, 22253377} Period: 12 The Riesel conjecture beats R280 for highest conjectured k, but I haven't searched very far so there might be a smaller one. Anyone want to see if there are any smaller Riesel or Sierp ks? (I can't be bothered ) Last fiddled with by 10metreh on 2011-02-19 at 18:46
 2011-02-23, 08:43 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 97·103 Posts A small update: At n<=75,000, R1031 still had 3 k's. I stopped it. S1031 has CK=302 and about a dozen k's after the script. Didn't run it. Last fiddled with by Batalov on 2011-02-23 at 09:25
2011-02-23, 09:48   #5
10metreh

Nov 2008

2×33×43 Posts

Attached are lists of the conjectured ks for the bases from 1031 to 1500.
I've tested all the bases with a CK of 4 to 2.5K (can't be bothered to go further as it's outside the scope of the project), and out of those, only 8 conjectures still have ks remaining. The work done on those bases is also attached (in the ck4 folder).
Attached Files
 conjto1500.zip (46.7 KB, 530 views)

2011-02-23, 12:46   #6
nuggetprime

Mar 2007
Austria

2·151 Posts

Quote:
 Originally Posted by Batalov I have tested R1031, CK 44. 3k remain at n=25,000. I would like to reserve it to 50K. Code: :::pl_trivial.txt::: 6 16 26 36 :::pl_prime.txt::: 2*1031^1722-1 12*1031^22-1 18*1031^3-1 20*1031^2-1 24*1031^2-1 28*1031^1-1 30*1031^3-1 32*1031^42-1 34*1031^1-1 38*1031^10-1 42*1031^236-1 22*1031^2897-1 40*1031^4273-1 14*1031^16166-1 :::pl_remain.txt::: 4*1031^n-1 8*1031^n-1 10*1031^n-1
Off topic, but why is 6 not the conjectured k for R1031 if it has trivial factors?

2011-02-23, 22:11   #7
gd_barnes

May 2007
Kansas; USA

2·7·827 Posts

Quote:
 Originally Posted by nuggetprime Off topic, but why is 6 not the conjectured k for R1031 if it has trivial factors?
It has only one trivial factor for all n-values: 5.

To be the conjectured k, a k must have two or more trivial factors to make the full covering set.

2011-02-25, 13:50   #8
10metreh

Nov 2008

2·33·43 Posts

Quote:
 Originally Posted by 10metreh Attached are lists of the conjectured ks for the bases from 1031 to 1500. I've tested all the bases with a CK of 4 to 2.5K (can't be bothered to go further as it's outside the scope of the project), and out of those, only 8 conjectures still have ks remaining. The work done on those bases is also attached (in the ck4 folder).
Found a better k (496311327760) for S1150 - missed it the first time because I only tested for primes up to 1e6 in the covering set and the new k has 1321351 in the set.
Here's an updated list of Sierp conjectures.
Attached Files
 sierpconj.txt (4.8 KB, 550 views)

2011-04-17, 11:51   #9
10metreh

Nov 2008

2×33×43 Posts

Here are the conjectured ks for bases 1501 to 2048.
Attached Files
 conj1501to2048.zip (4.9 KB, 537 views)

2011-06-17, 19:01   #10

Jan 2006
Hungary

22·67 Posts

Quote:
 Originally Posted by Batalov A small update: At n<=75,000, R1031 still had 3 k's. I stopped it.
I've also worked on base 1031, before I found the thread. Unsurprisngly, I found the same primes. After finding this thread, I skipped 25,000 < n < 75,000. And I was lucky:

Primality testing 10*1031^77187-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
10*1031^77187-1 is prime! (13348.8097s+0.0557s)

that leaves
4*1031^n-1
8*1031^n-1

I'll take these to n = 100,000.

Willem.

 2011-07-08, 21:57 #11 MyDogBuster     May 2008 Wilmington, DE B2416 Posts Risel & Sierp 1100-1199 I'd like to reserve Riesel & Sierp bases 1100-1199. Something to do in my spare time. Last fiddled with by MyDogBuster on 2011-07-08 at 21:58

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