This is the zip file for the status of all the started Sierpinski/Riesel bases b<=64.

Note 1: The file does not include R3 and R6, if you want the status for these two bases, please see [URL="https://www.rose-hulman.edu/%7Erickert/Compositeseq/"]https://www.rose-hulman.edu/~rickert/Compositeseq/[/URL].

Note 2: For bases S6, SR24, SR28, R30 and SR48, the file only include the k's such that gcd(k+-1,b-1) is not 1, if you want the status for the k's such that gcd(k+-1,b-1) = 1, please see the CRUS page: [URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm"]http://www.noprimeleftbehind.net/cru...onjectures.htm[/URL] (Sierpinski) and [URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm"]http://www.noprimeleftbehind.net/cru...onjectures.htm[/URL] (Riesel).

Note 3: For bases SR2, the file only include the k's <= 10000, if you want the status for the k's > 10000, please see [URL="http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm"]http://www.noprimeleftbehind.net/cru...es-powers2.htm[/URL] (Sierpinski), [URL="http://web.archive.org/web/20161028080202/http://www.prothsearch.net/sierp.html"]http://web.archive.org/web/201610280...net/sierp.html[/URL] (Sierpinski), [URL="http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm"]http://www.noprimeleftbehind.net/cru...es-powers2.htm[/URL] (Riesel), [URL]http://web.archive.org/web/20161028015217/http://www.prothsearch.net/rieselprob.html[/URL] (Riesel), [URL]https://www.rieselprime.de/[/URL] (both Sierpinski and Riesel).

Note 4: Bases SR15 and R36 are only started for the k's <= 10000, thus, the file only include the k's <= 10000 for these bases.

Note 5: The files list "algebra" if this k has full algebraic factors or partial algebraic factors, and all numbers of the form (k*b^n+-1)/gcd(k+-1,b-1) are composite. The file list "n (algebra)" if this k has full algebraic factors or partial algebraic factors, and the number (k*b^n+-1)/gcd(k+-1,b-1) is prime [I]only[/I] for this n.

Note 6: The files list "NA" if this k [I]may[/I] has primes, but there is no known (probable) primes for this k.

k-values that are a multiple of base (b) and where (k+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime are included in the conjectures but excluded from testing.
Such k-values will have the same prime as k / b.

These conjectures (for base b<=64) cannot be proven with current technology.

S2 (k=65536)
S6 (k=1296) (also k=7776 and k=46656, but they are excluded from testing)
S10 (k=100)
S12 (k=12) (also k=144, but it is excluded from testing)
S15 (k=225) (also k=3375 and k=50625, but they are excluded from testing)
S18 (k=18) (also k=324, but it is excluded from testing)
S22 (k=22) (also k=484, but it is excluded from testing)
S31 (k=1) (also k=31, but it is excluded from testing)
S32 (k=4)
S36 (k=1296)
S37 (k=37)
S38 (k=1)
S40 (k=1600)
S42 (k=42) (also k=1764, but it is excluded from testing)
S50 (k=1)
S52 (k=52) (also k=2704, but it is excluded from testing)
S55 (k=1)
S58 (k=58)
S60 (k=60) (also k=3600, but it is excluded from testing)
S62 (k=1)
S63 (k=1) (also k=63, but it is excluded from testing)

This is the zip file for the word file for the list of the CK, covering set, remain k, top 10 primes for the extended Sierpinski bases b<=32.
Next few days I will post the list of the CK, covering set, remain k, top 10 primes for the extended Riesel bases b<=32.
I will extend the list to the Sierpinski/Riesel bases b<=64 in the future.

Sierpinski:

2 78557 cover: {3, 5, 7, 13, 19, 37, 73} period=36
3 11047 cover: {2, 5, 7, 13, 73} period=12
4 419 cover: {3, 5, 7, 13} period=6
5 7 cover: {2, 3} period=2
6 174308 cover: {7, 13, 31, 37, 97} period=12
7 209 cover: {2, 3, 5, 13, 43} period=12
8 47 cover: {3, 5, 13} period=4
9 31 cover: {2, 5} period=2
10 989 cover: {3, 7, 11, 13} period=6
11 5 cover: {2, 3} period=2
12 521 cover: {5, 13, 29} period=4
13 15 cover: {2, 7} period=2
14 4 cover: {3, 5} period=2
15 673029 cover: {2, 17, 113, 1489} period=8
16 38 cover: {3, 7, 13} period=3
17 31 cover: {2, 3} period=2
18 398 cover: {5, 13, 19} period=4
19 9 cover: {2, 5} period=2
20 8 cover: {3, 7} period=2
21 23 cover: {2, 11} period=2
22 2253 cover: {5, 23, 97} period=4
23 5 cover: {2, 3} period=2
24 30651 cover: {5, 7, 13, 73, 79} period=12
25 79 cover: {2, 13} period=2
26 221 cover: {3, 7, 19, 37} period=6
27 13 cover: {2, 7} period=2
28 4554 cover: {5, 29, 157} period=4
29 4 cover: {3, 5} period=2
30 867 cover: {7, 13, 19, 31} period=6
31 239 cover: {2, 3, 7, 19} period=6
32 10 cover: {3, 11} period=2
33 511 cover: {2, 17} period=2
34 6 cover: {5, 7} period=2
35 5 cover: {2, 3} period=2
36 1886 cover: {13, 31, 37, 43} period=6
37 39 cover: {2, 19} period=2
38 14 cover: {3, 13} period=2
39 9 cover: {2, 5} period=2
40 47723 cover: {3, 7, 41, 223} period=6
41 8 cover: {3, 7} period=2
42 13372 cover: {5, 43, 353} period=4
43 21 cover: {2, 11} period=2
44 4 cover: {3, 5} period=2
45 47 cover: {2, 23} period=2
46 881 cover: {3, 7, 103} period=3
47 5 cover: {2, 3} period=2
48 1219 cover: {7, 13, 61, 181} period=6
49 31 cover: {2, 5} period=2
50 16 cover: {3, 17} period=2
51 25 cover: {2, 13} period=2
52 28674 cover: {5, 53, 541} period=4
53 7 cover: {2, 3} period=2
54 21 cover: {5, 11} period=2
55 13 cover: {2, 7} period=2
56 20 cover: {3, 19} period=2
57 47 cover: {2, 5, 13} period=4
58 488 cover: {3, 7, 163} period=3
59 4 cover: {3, 5} period=2
60 16957 cover: {13, 61, 277} period=4
61 63 cover: {2, 31} period=2
62 8 cover: {3, 7} period=2
63 1589 cover: {2, 5, 397} period=4
64 14 cover: {5, 13} period=2

Riesel:

2 509203 cover: {3, 5, 7, 13, 17, 241} period=24
3 12119 cover: {2, 5, 7, 13, 73} period=12
4 361 cover: {3, 5, 7, 13} period=6
5 13 cover: {2, 3} period=2
6 84687 cover: {7, 13, 31, 37, 97} period=12
7 457 cover: {2, 3, 5, 13, 19} period=12
8 14 cover: {3, 5, 13} period=4
9 41 cover: {2, 5} period=2
10 334 cover: {3, 7, 13, 37} period=6
11 5 cover: {2, 3} period=2
12 376 cover: {5, 13, 29}, period=4
13 29 cover: {2, 7} period=2
14 4 cover: {3, 5} period=2
15 622403 cover: {2, 17, 113, 1489} period=8
16 100 cover: {3, 7, 13} period=3
17 49 cover: {2, 3} period=2
18 246 cover: {5, 13, 19} period=4
19 9 cover: {2, 5} period=2
20 8 cover: {3, 7} period=2
21 45 cover: {2, 11} period=2
22 2738 cover: {5, 23, 97} period=4
23 5 cover: {2, 3} period=2
24 32336 cover: {5, 7, 13, 73, 577} period=12
25 105 cover: {2, 13} period=2
26 149 cover: {3, 7, 31, 37} period=6
27 13 cover: {2, 7} period=2
28 3769 cover: {5, 29, 157} period=4
29 4 cover: {3, 5} period=2
30 4928 cover: {13, 19, 31, 67} period=6
31 145 cover: {2, 3, 7, 19} period=6
32 10 cover: {3, 11} period=2
33 545 cover: {2, 17} period=2
34 6 cover: {5, 7} period=2
35 5 cover: {2, 3} period=2
36 33791 cover: {13, 31, 43, 97} period=6
37 29 cover: {2, 5, 7, 13, 67} period=12
38 13 cover: {3, 5, 17} period=4
39 9 cover: {2, 5} period=2
40 25462 cover: {3, 7, 41, 223} period=6
41 8 cover: {3, 7} period=2
42 15137 cover: {5, 43, 353} period=4
43 21 cover: {2, 11} period=2
44 4 cover: {3, 5} period=2
45 93 cover: {2, 23} period=2
46 928 cover: {3, 7, 103} period=3
47 5 cover: {2, 3} period=2
48 3226 cover: {5, 7, 461} period=4
49 81 cover: {2, 5} period=2
50 16 cover: {3, 17} period=2
51 25 cover: {2, 13} period=2
52 25015 cover: {3, 7, 53, 379} period=6
53 13 cover: {2, 3} period=2
54 21 cover: {5, 11} period=2
55 13 cover: {2, 7} period=2
56 20 cover: {3, 19} period=2
57 144 cover: {5, 13, 29} period=4
58 547 cover: {3, 7, 163} period=3
59 4 cover: {3, 5} period=2
60 20558 cover: {13, 61, 277} period=4
61 125 cover: {2, 31} period=2
62 8 cover: {3, 7} period=2
63 857 cover: {2, 5, 397} period=4
64 14 cover: {5, 13} period=2

These k's have algebraic factors and should be excluded from the conjectures: (for Sierpinski/Riesel bases b<=64)

S8: all k = m^3
S16: all k = 4*m^4
S27: all k = m^3
S32: all k = m^5
S64: all k = m^3
R4: all k = m^2
R8: all k = m^3
R9: all k = m^2
R12: all k = m^2 and m = 5 or 8 mod 13, and all k = 3*m^2 and m = 3 or 10 mod 13
R14: all k = m^2 and m = 2 or 3 mod 5, and all k = 14*m^2 and m = 2 or 3 mod 5
R16: all k = m^2
R19: all k = m^2 and m = 2 or 3 mod 5, and all k = 19*m^2 and m = 2 or 3 mod 5
R24: all k = m^2 and m = 2 or 3 mod 5, and all k = 6*m^2 and m = 1 or 4 mod 5
R25: all k = m^2
R27: all k = m^3
R28: all k = m^2 and m = 12 or 17 mod 29, and all k = 7*m^2 and m = 5 or 24 mod 29
R30: k = 1369 (for k < 4928)
R32: all k = m^5
R33: all k = m^2 and m = 4 or 13 mod 17, and all k = m^2 and m = 15 or 17 mod 32, and all k = 33*m^2 and m = 4 or 13 mod 17, and all k = 33*m^2 and m = 15 or 17 mod 32
R34: all k = m^2 and m = 2 or 3 mod 5, and all k = 34*m^2 and m = 2 or 3 mod 5
R36: all k = m^2
R38: all k = m^2 and m = 5 or 8 mod 13, and all k = 38*m^2 and m = 5 or 8 mod 13
R39: all k = m^2 and m = 2 or 3 mod 5, and all k = 39*m^2 and m = 2 or 3 mod 5
R40: all k = m^2 and m = 9 or 32 mod 41, and all k = 10*m^2 and m = 18 or 23 mod 41
R44: all k = m^2 and m = 2 or 3 mod 5, and all k = 11*m^2 and m = 1 or 4 mod 5
R49: all k = m^2
R50: all k = m^2 and m = 4 or 13 mod 17, and all k = 2*m^2 and m = 3 or 14 mod 17
R51: all k = m^2 and m = 5 or 8 mod 13, and all k = 51*m^2 and m = 5 or 8 mod 13
R52: all k = m^2 and m = 23 or 30 mod 53, and all k = 13*m^2 and m = 7 or 46 mod 53
R54: all k = m^2 and m = 2 or 3 mod 5, and all k = 6*m^2 and m = 1 or 4 mod 5
R57: all k = m^2 and m = 12 or 17 mod 29, and all k = m^2 and m = 3 or 5 mod 16, and all k = 57*m^2 and m = 12 or 17 mod 29, and all k = 57*m^2 and m = 3 or 5 mod 16
R59: all k = m^2 and m = 2 or 3 mod 5, and all k = 59*m^2 and m = 2 or 3 mod 5
R60: all k = m^2 and m = 11 or 50 mod 61, and all k = 15*m^2 and m = 22 or 39 mod 61
R64: all k = m^2, and all k = m^3

This is the zip file for the word file for the list of the CK, covering set, remain k, top 10 primes for the extended Sierpinski/Riesel bases b<=32.

Corrected the error in R27 for the file. (k=1 has algebraic factors for R27)

(11*64^3222+1)/3 is a probable prime!!!

Extended S64 is proven!!!

Corrected the k and n for the top 10 primes for extended R3. (some k's for the primes are divisible by 3 and (k-1)/gcd(k-1,3-1) is not prime, these k's should divide by 3. In fact, these primes were correct, but we should use the right k for the primes. (i.e. we should not use the k's excluded from testing for the primes)

k-values that are a multiple of base (b) and where gcd(k+-1,b-1) is not prime are included in the conjectures but excluded from testing, since such k-values will have the same prime as k / b.

I reserved R33 and R43 (the Riesel bases 33<=b<=64 with only few k's remain), no (probable) prime found, these two bases were likely tested to n=5000.

Reserve S33, S37, S55, S61 (the Sierpinski bases 33<=b<=64 with only few k's remain).

(S38, S50 and S62 were tested to at least n=2^24-1, S36 was tested to at least n=5000, and S53 was tested to n=750000, all have no prime found)

Also reserve R61 to n=2000.