Riesel base 347, k=28
Primes:
2*347^522-1
4*347^3-1
6*347^1-1
8*347^4-1
10*347^1-1
12*347^5-1
16*347^9-1
18*347^10-1
20*347^2-1
24*347^384-1
26*347^18-1
14*347^4616-1

Remaining k's:
22*347^n-1

Base completed to 25K and released.

New base S482 k=8 conjecture is complete to n=25K. Only k=4 remains.

Riesel bases 305 and 407
 

Primes found:

2*305^2-1
4*305^3-1
6*305^2-1
8*305^2-1
10*305^1-1
12*305^1-1
14*305^2-1

2*407^10-1
4*407^1-1
6*407^1-1
10*407^345-1
12*407^5-1
14*407^452-1

k=8 has trivial factors. With a conjectured k of 16, both of these conjectures are proven.

[LEFT]Reserving Riesel 337 and 423 as new to n=25K
[/LEFT]

Riesel base 286
 

Primes found:

[code]
2*286^1-1
3*286^1-1
5*286^1-1
8*286^1-1
9*286^163-1
12*286^3-1
14*286^1-1
15*286^1-1
17*286^1-1
18*286^1-1
23*286^1-1
24*286^1-1
27*286^2-1
29*286^1-1
30*286^3-1
32*286^1-1
33*286^1-1
35*286^1-1
38*286^1-1
42*286^1-1
44*286^1-1
45*286^4-1
47*286^1-1
48*286^6-1
50*286^3-1
53*286^6-1
54*286^1-1
57*286^1-1
59*286^2-1
60*286^1-1
62*286^2-1
63*286^3-1
65*286^2-1
68*286^1-1
69*286^2-1
72*286^8-1
74*286^1-1
75*286^2-1
78*286^1-1
80*286^2-1
[/code]

The conjectured k is 83. All other k have trivial factors. The conjecture is proven.

I don't think that I've seen another conjecture with so many small n.

Riesel base 426
 

Primes found:

[code]
2*426^2-1
3*426^1-1
4*426^3-1
5*426^1-1
7*426^60-1
8*426^1-1
9*426^1-1
10*426^1-1
12*426^29-1
13*426^2-1
14*426^2-1
15*426^1-1
17*426^4-1
19*426^1-1
20*426^2-1
22*426^1-1
23*426^2-1
24*426^1-1
25*426^13-1
27*426^4-1
28*426^1-1
29*426^49-1
30*426^4-1
32*426^6-1
33*426^1-1
34*426^6-1
37*426^1-1
38*426^1-1
39*426^3-1
40*426^19-1
42*426^1-1
43*426^3-1
44*426^1-1
45*426^13-1
47*426^1-1
48*426^2-1
49*426^1-1
50*426^5-1
53*426^15-1
54*426^1-1
55*426^162-1
57*426^1-1
58*426^2-1
59*426^5-1
60*426^8-1
[/code]

The conjectured k is 62. The other k have trivial factors. This conjecture is proven.

Reserving Sierp 338 and 343 as new to n=25K

Reserving Riesel 253 and 268 as new to n=25K

[QUOTE=Siemelink;211366]Hi folks,

I've run the numbers on Riesel base 308. There are 7 k's left at n = 25,000:
7*308^n-1
43*308^n-1
52*308^n-1
59*308^n-1
67*308^n-1
74*308^n-1
89*308^n-1

Regards, Willem.[/QUOTE]
Here is the missing bit:
101*308^90-1
102*308^4-1
103*308^1-1

Regards, Willem.

Riesel Base 337
 

Riesel Base 337
Conjectured k = 378
Covering Set = 5, 13, 41
Trivial Factors k == 1 mod 2(2)
k == 1 mod 3(3)
k == 1 mod (7(7)

Found Primes: 103k's - File attached

Remaining k's: 3k's - Tested to n=25K
38*337^n-1
194*337^n-1
222*337^n-1

k=324 proven composite by partial algebraic factors

Trivial Factor Eliminations: 81k's

Base Released

Reserving Riesel 387 & 390 as new to n=25K