Riesel Base 818
 

Primes found:

2*818^2-1
3*818^4-1
4*818^1-1
5*818^4-1
6*818^2-1
7*818^3-1

k=1 has trivial factors. The conjecture is proven

Riesel base 797
 

Primes found:

2*797^2-1
4*797^1-1
6*797^2-1

This conjecture is proven.

Riesel Base 776
 

Primes found:

2*776^4-1
3*776^2-1
4*776^3-1
5*776^12-1
7*776^1-1

k=1 and k=6 have trivial factors. This conjecture is proven.

Riesel Base 762
 

Primes found:

2*762^1-1
3*762^116-1
4*762^7-1
5*762^4-1
6*762^2-1
7*762^1-1

k=1 has trivial factors. This conjecture is proven.

Riesel Base 755
 

Primes found:

2*755^62-1
4*755^1-1
6*755^18-1

The conjecture is proven.

Riesel Base 520
 

The primes are attached.

These k remain
[code]
179*520^n-1
216*520^n-1
324*520^n-1
330*520^n-1
576*520^n-1
638*520^n-1
1094*520^n-1
[/code]

The other k have trivial factors.

I have tested to n=25000 and am releasing the base.

From my former k=2 search:

R515 is complete to n=25K; only k=2 remains; base released.

I'll take Riesel base 515 and see if I can prove it.

2*515^58466-1 is prime.

This prove the Riesel conjecture for base 515 and takes one off the list.

Taking Sierpinski base 969 with conjectured k = 96.

BTW, I proved Riesel conjecture for base 515. 2*515^58466-1 is prime.

Sierpinski base 969
 

Primes found:

[code]
2*969^4+1
4*969^1+1
6*969^5888+1
8*969^1+1
12*969^8+1
14*969^1+1
16*969^16+1
18*969^1+1
20*969^1+1
22*969^1+1
24*969^83+1
26*969^8714+1
28*969^5+1
30*969^24+1
34*969^5+1
36*969^2+1
38*969^3+1
40*969^12+1
42*969^1+1
44*969^107+1
46*969^56+1
48*969^8+1
50*969^6+1
52*969^621+1
56*969^4+1
58*969^2+1
60*969^4+1
62*969^2+1
64*969^1+1
66*969^1068+1
68*969^8+1
70*969^2+1
72*969^2+1
74*969^1+1
78*969^1+1
80*969^1+1
82*969^2+1
84*969^5+1
86*969^90+1
88*969^9+1
90*969^1+1
92*969^7+1
94*969^113+1
[/code]

The other k have trivial factors.

This conjecture is proven.