These k's for these Sierpinski bases cannot be eliminated with current technology, since they are GFN's or half GFN's without known (probable) primes. (include the k's > CK, but not include the k's without from testing, i.e. k's that are multiples of base (b) and where (k+1)/gcd(k+1,b-1) is not prime)

[CODE]
base k
2 65536
3 3433683820292512484657849089281
4 65536
5 625
6 1296
7 2401
8 256, 65536
9 3433683820292512484657849089281
10 100
11 14641
12 12
13 815730721
14 196
15 225
16 65536
17 83521
18 18
19 361
20 160000
21 2046526777500669368329342638102622164679041
22 22
23 279841
24 331776
25 625
26 676
27 1853020188851841, 3433683820292512484657849089281
28 614656
29 250246473680347348787521
30 185302018885184100000000000000000000000000000000
31 1
32 4, 16, 256, 65536
33 1406408618241
34 1336336
35 661233485303375668149836762254674220999159684294975425898101273336493477472686208784580230712890625
36 1296
37 37
38 1
39 2313441
40 1600
41 63759030914653054346432641
42 42
43 11688200277601
44 197352587024076973231046656
45 2025
46 46^512
47 23811286661761
48 5308416
49 2401
50 1
51 19252683449641888890260123354856276823237618025475304982087581524852141411154717334003958315833698636313043201
52 52
53 62259690411361
54 27327525884414205519790497974303154461449992065060438016
55 1
56 9834496
57 10556001
58 58
59 3481
60 60
61 13845841
62 1
63 1
64 256, 65536
65 10309258098174834118790766041464760922826826572418212890625
66 4356
67 1
68 1
69 513798374428641
70 70
71 71^16384
72 72
73 650377879817809571042122834561
74 808551180810136214718004658176
75 1004524257206332858195774182519244277500547468662261962890625
76 1238846438084943599707227160576
77 1
78 78
79 6241
80 40960000
81 3433683820292512484657849089281
82 45212176
83 1
84 7056
85 3039563674866725366216700431136500455038221930406808846390168104209843587706907906166586830210007974528707563877105712890625
86 1
87 10772290133751755506346104768641
88 59969536
89 1
90 65610000
91 1
92 1
93 93
94 37157429083410091685945089785856
95 9025
96 2708192040014184559945134363758220403329915059847434832829218816
97 1
98 1
99 1
100 100
101 10201
102 102^64
103 112550881
104 1
105 121550625
106 126247696
107 1
108 108
109 1
110 12100
111 531089433205482293807404177813761
112 375817263084708503965641077546115954135779496817219617550715846656
113 113^128
114 662148260948741787228316709317924977225312314678010411233675575296
115 174900625
116 13456
117 117
118 37588592026706176
119 200533921
120 120^128
121 14641
122 1
123 1
124 15376
125 25, 625
126 15876
127 1
128 16, 256, 65536
256 65536
512 2, 4, 16, 32, 256, 65536
1024 4, 16, 256, 65536
[/CODE]

[QUOTE=sweety439;465523]These k's for these Sierpinski bases cannot be eliminated with current technology, since they are GFN's or half GFN's without known (probable) primes. (include the k's > CK, but not include the k's without from testing, i.e. k's that are multiples of base (b) and where (k+1)/gcd(k+1,b-1) is not prime)[/QUOTE]

If we do not include the k's > CK, then they are:

[CODE]
base k
2 65536
6 1296
10 100
12 12
15 225
18 18
22 22
31 1
32 4
36 1296
37 37
38 1
40 1600
42 42
50 1
52 52
55 1
58 58
60 60
62 1
63 1
66 4356
67 1
68 1
70 70
72 72
77 1
78 78
83 1
86 1
89 1
91 1
92 1
93 93
97 1
98 1
99 1
104 1
107 1
108 108
109 1
117 117
122 1
123 1
124 15376
126 15876
127 1
128 16
512 2, 4, 16
1024 4, 16
[/CODE]

[QUOTE=sweety439;460659]These are the text files for R70 and R88, tested to n=1000.[/QUOTE]

Found some primes in CRUS (i.e. gcd(k-1,b-1) = 1) for R88.

17*88^1362-1
68*88^2477-1
89*88^1704-1
179*88^4545-1
212*88^5511-1
380*88^8712-1
444*88^19708-1
464*88^20648-1
477*88^5816-1
522*88^1108-1
536*88^1731-1

Found some primes in CRUS (i.e. gcd(k-1,b-1) = 1) for R70.

278*70^1320-1
434*70^3820-1
489*70^2096-1
729*70^28625-1

Update newest text files for Sierpinski/Riesel conjectures bases <= 128 (except R3, R6, SR40, SR52, SR66, S70, SR78, SR82, SR96, R106, SR120, SR124, SR126, S127) and bases 256, 512 and 1024.

[QUOTE=sweety439;465371]The first few bases remain at n=1024 for these k's are:

[B]Sierpinski k=1:[/B]

31, 38, 50, 55, 62, 63, 67, 68, 77, 83, 86, 89, 91, 92, 97, 98, 99, 104, 107, 109, 122, 123, 127, 135, 137, 143, 144, 147, 149, ...

[B]Sierpinski k=2:[/B]

38, 101, 104, 167, 206, 218, 236, 257, 287, 305, ...

[B]Sierpinski k=3:[/B]

83, 123, 191, 261, 293, 303, ...

[B]Sierpinski k=4:[/B]

32, 53, 77, 83, 107, 113, 155, 161, 174, 204, 206, 212, 227, 230, ...

[B]Riesel k=1:[/B]

51, 91, 135, 142, 152, 174, 184, 185, 200, 230, 244, 259, 269, 281, 284, 311, ...

[B]Riesel k=2:[/B]

107, 170, 215, 233, 254, 276, 278, 298, 303, 380, 382, 383, ...

[B]Riesel k=3:[/B]

42, 107, 159, 283, 295, 347, 359, ...

[B]Riesel k=4:[/B]

47, 72, 115, 163, 167, 178, 212, 218, 223, 232, 240, 270, ...[/QUOTE]

Some known (probable) primes with bases b<=512 and n>1024 for these k's:

[CODE]
Sierpinski k=2:

38 (2729)
101 (192275)
104 (1233)
167 (6547)
206 (46205)
236 (161229)
257 (12183)
287 (5467)
305 (16807)
353 (2313)
368 (7045)
395 (2625)
416 (2517)
467 (126775)
497 (1339)

Sierpinski k=3:

358 (9560)
424 (1105)

Sierpinski k=4:

77 (6098)
83 (5870)
107 (32586)
113 (2958)
227 (13346)
242 (4206)
257 (160422)
264 (9647)
293 (1034)
308 (1966)
353 (2086)
355 (10989)
410 (144078)
422 (2634)
440 (56086)
452 (14154)
470 (5218)
482 (30690)
497 (1898)

Riesel k=1:

51 (4229)
91 (4421)
135 (1171)
142 (1231)
152 (270217)
174 (3251)
184 (16703)
230 (5333)
244 (3331)
259 (2011)
284 (2473)
318 (1193)
333 (9743)
360 (2609)
375 (1993)
376 (1223)
391 (9623)
411 (1061)
454 (1217)
469 (5987)
487 (9967)
499 (4691)

Riesel k=2:

107 (21910)
170 (166428)
215 (1072)
233 (8620)
254 (2866)
276 (2484)
278 (43908)
298 (4202)
303 (40174)
380 (3786)
382 (2324)
383 (20956)
434 (1166)

Riesel k=3:

42 (2523)
432 (16002)
446 (4850)

Riesel k=4:

47 (1555)
72 (1119849)
115 (4223)
163 (2285)
167 (1865)
212 (34413)
218 (23049)
240 (1401)
270 (89661)
380 (2039)
422 (21737)
461 (3071)
480 (93609)
491 (1683)
498 (2527)
512 (2215)
[/CODE]

Sierpinski base 131
 

[CODE]
k,n
1,2
2,1
3,1
4,2
[/CODE]

With conjectured k=5, this conjecture is proven.

Sierpinski base 134
 

[CODE]
k,n
1,2
2,1
3,4
[/CODE]

With conjectured k=4, this conjecture is proven.

Sierpinski base 139
 

[CODE]
k,n
1,2
2,5
3,3
4,1
5,6
[/CODE]

With conjectured k=6, this conjecture is proven.

Sierpinski base 143
 

[CODE]
k,n
2,5
3,183
4,10
[/CODE]

With conjectured k=5, k=1 remains.

Sierpinski base 146
 

[CODE]
k,n
1,2
2,1
3,1
4,2
5,3
6,1
7,2
[/CODE]

With conjectured k=8, this conjecture is proven.