20080712, 19:59  #12  
May 2007
Kansas; USA
10100001000111_{2} Posts 
Quote:
In other words, it's best if everything is sorted by k except for the trivial k's. Example on some fictional base: Code:
k==(1 mod 3) is trivial k prime/status 2 5 3 remaining 5 1 6 3 8 2 9 algebraic factors 11 remaining etc. up to the conjectured kvalue This accounts for everything in a nutshell. Alternatively, if the algebraic factors are very consistent (which they frequently are not like on base 33), you can just state something like "k's that are a perfect square have algebraic factors" and not show those in the list of k's. Gary Last fiddled with by gd_barnes on 20080712 at 20:01 

20080713, 12:34  #13 
Jan 2006
Hungary
2^{2}×67 Posts 
base 49 PRPs
1394*49^526981
1266*49^361911 230*49^248241 1706*49^163371 1784*49^134801 786*49^63931 I am running PFGW on these at the moment, the confirmation will follow later. Willem. 
20080713, 13:24  #14  
May 2007
Kansas; USA
3·7·491 Posts 
Quote:
It looks like you may be in top5000 territory (i.e. n>60K) on the last k. Good luck with it! Gary 

20080713, 14:32  #15  
Jan 2006
Hungary
2^{2}·67 Posts 
Quote:
By now the six primes were confirmed by PFGW. Willem. 

20080720, 10:51  #16 
Jan 2006
Hungary
2^{2}×67 Posts 
Riesel base 48
The riesel conjecture for base 48 = 4208, with cover set {7, 13, 37, 61}
Even => 7 6m+1 => 13 6m+3 => 37 6m+5 => 61 checked n upto 10000 total k 4117 total p 4043 Remaining k 74 I've checked the 4043 primes with pfgw, they all hold up. Of the remaining k, two are squares but I couldn't eliminate them. There is one k that can be divided by 48. but I coudn't eliminate that one either. Top ten primes 1422 9235 3179 9107 1021 8570 4108 8296 3382 7927 1103 7918 475 7424 2449 7244 3907 7083 3541 7078 All the k's and primes are in the attachment. Feel free to find more primes. Enjoy, Willem. 
20080720, 11:01  #17 
Jan 2006
Hungary
2^{2}×67 Posts 
Riesel base 39 & 40
The lowest Riesel for base 39 = 1,352,534, with covering set {5, 7, 223, 1483}.
The lowest Riesel for base 40 = 3,386,517, with covering set {7, 41, 223, 547}. I've calculated these with my riesel generator, but I didn't generate any k. If you feel like generating a lot of primes, here is your chance. Willem. 
20080720, 19:55  #18 
May 2007
Kansas; USA
10100001000111_{2} Posts 
Thanks Willem. Your base 48 info. is exactly what we need on a new base...covering set and all.
One thing I'll add for everyone's reference: Willem has correctly removed all k==(1 mod 47) remaining, which have a trivial factor of...you guessed it...47. Gary Last fiddled with by gd_barnes on 20080720 at 20:00 
20080721, 11:19  #19 
May 2007
Kansas; USA
3×7×491 Posts 
Willem,
What is your search limit on k=2186 for Sierp base 49 and how high were you going to take it? I have used n=5K because that was how high I searched it to get all of the small primes for the base. I assume you've searched it somewhere above n=50K since you have a prime for k=1394 at n=52698. Thanks, Gary 
20080721, 12:14  #20  
Jan 2006
Hungary
10C_{16} Posts 
Quote:
Willem. 

20080723, 21:06  #21 
Jan 2006
Hungary
2^{2}·67 Posts 
Riesel base 46
Hi everyone,
here is my effort on Riesel base 46. The conjectured lowest riesel is 8177. The cover set is {29, 47, 73}. While generating the k's I've ignored even k's and k mod 23 = 1. At n = 10,000 there are 22 k's left: 93 800 870 1317 1362 2819 3147 3194 3383 3812 4419 4580 5940 6060 6062 6297 7157 7284 7424 7472 7520 7848 I've checked against squares, there are none left. k = 4278 = 93 *48 and 93 is still in the list. That allows me te remove k = 4278. The top ten of primes is: 6224 8837 4464 7100 3504 4377 6524 3504 7715 3482 1940 3473 5979 3275 2042 3010 4610 2724 6263 2372 All the primes have been tested with pfgw and are attached. Find some more! Willem. 
20080725, 07:02  #22  
May 2007
Kansas; USA
3×7×491 Posts 
Quote:
Ignoring k==(1 mod 23) would be for Riesel base 47. We would never ignore even k's. Gary Last fiddled with by gd_barnes on 20080725 at 07:06 

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