mersenneforum.org Generalized Prime Riesel Conjectures
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2008-11-30, 15:53   #1

Jan 2006
Hungary

22×67 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.
Attached Files
 PRiesel.zip (210.4 KB, 342 views)

 2008-12-01, 10:18 #2 kar_bon     Mar 2006 Germany 2×32×7×23 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 102430000 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!
 2008-12-02, 21:27 #3 gd_barnes     May 2007 Kansas; USA 5·31·67 Posts Very interesting efforts guys. Karsten, I had attempted such an effort for Riesel base 2 for k=509205-600000 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 50-125 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
 2017-05-18, 16:52 #4 sweety439     Nov 2016 285510 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 2017-05-18 at 16:53
2017-05-23, 18:44   #5
sweety439

Nov 2016

5×571 Posts

Quote:
 Originally Posted by sweety439 Are there any project for the generalized prime Sierpinski conjectures? Of course, for base 2, this CK is 271129.
base primeSierpinski
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 2017-05-23 at 18:46 Reason: k=188299 is also trivial in S6 :)

 2017-06-19, 15:41 #6 sweety439     Nov 2016 5·571 Posts @Gary, do you decide to solve the generalized prime Sierpinski/Riesel conjectures?
 2020-08-05, 00:11 #7 sweety439     Nov 2016 5×571 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 Prime Riesel: 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 (I searched to k=5M, and the CK for S40 is given by post #1)

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