Base 16
 

Ok, here are the next few candidates for 16, all tested to n=4295. Last k tested was 47805

27592
27838
28593
28918
29445
30250
30397
31347
31912
32161
32350
32556
32673
33661
33771
34528
34543
35257
35320
35548
35818
35845
36735
37372
38440
38562
38776
39322
39337
39781
40000
40410
41530
42052
42376
42717
42745
43368
43398
43468
43485
44035
44131
44490
45306
45712
46471
46528
47176
47298
47395
47482
47616

Base 16 Sierpinski
 

And here is the last batch of Sierpinski 16, tested to n=5098

47818
48697
48772
48976
49386
49860
50166
50863
50865
51171
51427
52072
53226
53653
53941
54610
55306
55611
55846
55897
56866
57238
57795
57867
58582
58791
58855
59890
60070
60343
60541
60891
61617
61687
62802
63390
63405
63411
63853
64518
64620
65077
65127
65397
65536 square
65623

In post 112, k=40000 is square

[QUOTE=robert44444uk;97130]In post 112, k=40000 is square[/QUOTE]


You did not exclude numbers divisible by 16:grin:

Sierpinski 16
 

I will reserve those above k=60000 and take them quite high

[QUOTE=Citrix;97131]You did not exclude numbers divisible by 16:grin:[/QUOTE]

True, can you spot them and weed them out

Base 16 Sierpinski
 

Doing a quick check through the top 5000 site

42717*2^905792+1 is prime! L159 2005
44131*2^995972+1 is prime! SB3 2002 - very valuable "Seventeen or Bust", a first prime for 44131 and so this will save man years of work

Base 18 Sierpinski
 

Unreserving Base18 Sierpinski

k=122 tested till n=110746
no primes found - anyone else want to try?

381*18^24108+1 is a probable prime.
Do I have to register this prime somewhere? Prime Pages says, it is too small.

k=18 and k=324
stopped testing, because k = base

[quote=Xentar;97217]
381*18^24108+1 is a probable prime.
Do I have to register this prime somewhere? Prime Pages says, it is too small.
[/quote]



Simply no.

Base 12 Sierpinski
 

Prof Caldwell has pointed out an error in the k value quoted for Base 12 Sierpinski, due to me choosing the wrong covering set to analyse.

In fact the covering set 5,13,29 produces a Sierpinski at k=521, and nominal sieving leaves 261,378 and 404 to find primes for, in addition to the GFN k's 12 and 144.

Recalculating gives the Riesel at 376, with the following unfound at n=5000

25,27,64,300,324 which are all highly composite (all 2,3, and 5), I will leave it to others to demonstrate that these factor (I am feeling lazy today)

Base 16 Sierpinski
 

I looked at the base 16 sierpinski for all k >60000, report as follows:

k n prime

60343 5745
60541 44085
60891 10036
61617 7845
61687 8948
62802 42004
63390 23511
63411 18016
64518 36998
65127 5206
65397 6222

No primes were found for the following k, tested up to the following n:

60070 53562
63405 42335
63853 39256
64620 75696
65077 58138
65623 64630

Will reserve all between k=50000 and k=60000