20081130, 15:53  #1 
Jan 2006
Hungary
100001100_{2} Posts 
Generalized Prime Riesel Conjectures
Hi everyone,
Here is what I have been busy with for the last few months. I've been trying to prove conjectures that are prime and then only the k's that are prime. For base 2 that is the same as the existing Prime Riesel Prime search. I've been looking at those with other bases: base primeRiesel 2...........509,203 4...........2,251,349 6...........429,127 8...........307.........Proven 10..........72,953 12..........6,397 14..........11..........Proven 16..........313,517 18..........1,481......Proven 20..........13..........Proven 22..........93,701 24..........335,411 26..........149.........Proven 28..........231,419 30..........11,471 32..........23..........Proven 34..........29..........Proven 36..........429,127 38..........13..........Proven 40..........42,970,133 42..........15,137 44..........11..........Proven 46..........288,203 48..........8,807 50..........67 I've attached my result sheet, that's easier to read. A natural location for this would be on Gary's CRUS page. But I haven't gone all out on the double checking, so the contents may be not 100% correct. Enjoy, Willem. 
20081201, 10:18  #2 
Mar 2006
Germany
2878_{10} Posts 
nice table!
for information: i've found data about the extension of the Riesel Prime Conjecture upto n=10^7. the data includes all first primes 1024<n<30000 for the k's. i'm testing n>30000 and doublecheking all lower values. there're about 5600 k's without a prime for 509203<=k<=10^7 and many k's with Nash weight=0. when doubleckeck is ok, i'll put a new page on rieselprime.de! 
20081202, 21:27  #3 
May 2007
Kansas; USA
2×5×1,031 Posts 
Very interesting efforts guys.
Karsten, I had attempted such an effort for Riesel base 2 for k=509205600000 up to n=25K. I have the info. but obviously it's a small duplication of what you are doing. Willem, I won't easily be able to show your info. on the pages as currently designed. I'll make a note of it on my task list but it will likely be several months before I'm able to get to it. In the mean time, I've done some searches for Riesel bases 50125 recently. I'll post a cursory sampling of what I've done in another thread today so that no one duplicates my effort. I chose most of the bases that were relatively easy to prove and a few that will be a little more difficult to keep things interesting. Gary 
20170518, 16:52  #4 
Nov 2016
5404_{8} Posts 
Are there any project for the generalized prime Sierpinski conjectures?
Of course, for base 2, this CK is 271129. Last fiddled with by sweety439 on 20170518 at 16:53 
20170523, 18:44  #5  
Nov 2016
2^{2}×3×5×47 Posts 
Quote:
2.........271129 4.........271129 6.........7075837 8.........47.............Proven 10.......48247 12.......521...........Proven 14.......11.............Proven 16.......3608251 18.......571...........Proven 20.......13.............Proven Last fiddled with by sweety439 on 20170523 at 18:46 Reason: k=188299 is also trivial in S6 :) 

20170619, 15:41  #6 
Nov 2016
101100000100_{2} Posts 
@Gary, do you decide to solve the generalized prime Sierpinski/Riesel conjectures?

20200805, 00:11  #7 
Nov 2016
2^{2}×3×5×47 Posts 
Found more CK:
Prime Sierpinski: Code:
b,CK 2,271129 4,271129 6,282001 8,47 10,48247 12,521 14,11 16,2202997 18,571 20,13 22,30727 24,534301 26,1627 28,8293 30,18973 32,23 34,181 36,11093 38,53 40,826477 42,350881 44,11 46,51511 48,5531 50,67 52,260761 54,89 56,37 58,211573 60,199103 62,13 64,79 Code:
b,CK 2,509203 4,2251349 6,429127 8,307 10,72953 12,6397 14,11 16,313517 18,1481 20,13 22,93701 24,335411 26,149 28,231419 30,11471 32,23 34,29 36,429127 38,13 40,42970133 42,15137 44,11 46,288203 48,8807 50,67 52,599429 54,89 56,37 58,1429451 60,1013819 62,13 64,311 
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