mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > Conjectures 'R Us

Reply
 
Thread Tools
Old 2010-12-23, 21:17   #1
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×11×307 Posts
Default 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
gd_barnes is offline   Reply With Quote
Old 2011-01-07, 04:29   #2
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3

2·3·5·7·43 Posts
Default

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
Batalov is offline   Reply With Quote
Old 2011-02-19, 18:45   #3
10metreh
 
10metreh's Avatar
 
Nov 2008

2·33·43 Posts
Default 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
10metreh is offline   Reply With Quote
Old 2011-02-23, 08:43   #4
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3

2×3×5×7×43 Posts
Default

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
Batalov is offline   Reply With Quote
Old 2011-02-23, 09:48   #5
10metreh
 
10metreh's Avatar
 
Nov 2008

2×33×43 Posts
Default

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
File Type: zip conjto1500.zip (46.7 KB, 168 views)
10metreh is offline   Reply With Quote
Old 2011-02-23, 12:46   #6
nuggetprime
 
nuggetprime's Avatar
 
Mar 2007
Austria

2×151 Posts
Default

Quote:
Originally Posted by Batalov View Post
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?
nuggetprime is offline   Reply With Quote
Old 2011-02-23, 22:11   #7
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

3×11×307 Posts
Default

Quote:
Originally Posted by nuggetprime View Post
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.
gd_barnes is offline   Reply With Quote
Old 2011-02-25, 13:50   #8
10metreh
 
10metreh's Avatar
 
Nov 2008

44228 Posts
Default

Quote:
Originally Posted by 10metreh View Post
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
File Type: txt sierpconj.txt (4.8 KB, 237 views)
10metreh is offline   Reply With Quote
Old 2011-04-17, 11:51   #9
10metreh
 
10metreh's Avatar
 
Nov 2008

2·33·43 Posts
Default

Here are the conjectured ks for bases 1501 to 2048.
Attached Files
File Type: zip conj1501to2048.zip (4.9 KB, 161 views)
10metreh is offline   Reply With Quote
Old 2011-06-17, 19:01   #10
Siemelink
 
Siemelink's Avatar
 
Jan 2006
Hungary

22×67 Posts
Default

Quote:
Originally Posted by Batalov View Post
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.
Siemelink is offline   Reply With Quote
Old 2011-07-08, 21:57   #11
MyDogBuster
 
MyDogBuster's Avatar
 
May 2008
Wilmington, DE

283610 Posts
Default 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
MyDogBuster is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Bases 501-1030 reservations/statuses/primes KEP Conjectures 'R Us 3668 2020-05-31 06:11
k*b^n+/-1, Bases 271 and 11971 robert44444uk Math 21 2013-11-07 15:01
Other Bases? wblipp GPU Computing 50 2012-10-11 13:23
Numbers in Other Bases Stargate38 Lounge 21 2011-09-21 03:34
Starting new bases MrOzzy Conjectures 'R Us 104 2010-03-18 22:11

All times are UTC. The time now is 06:44.

Sat Jun 6 06:44:35 UTC 2020 up 73 days, 4:17, 0 users, load averages: 0.65, 0.90, 0.92

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.