Riesel base 557, k=32
Primes:
2*557^8-1
4*557^27-1
6*557^2-1
8*557^112-1
10*557^1-1
12*557^9-1
16*557^9-1
18*557^7-1
20*557^8-1
22*557^1-1
24*557^1-1
14*557^1364-1
28*557^3207-1
30*557^22290-1

1 k's remain: 26*557^n-1
Base completed to 25K and released.

Riesel base 853
 

Primes found:

2*853^4-1
6*853^234-1
8*853^1-1
12*853^244-1
14*853^1-1
18*853^6-1
20*853^2-1
24*853^3-1
26*853^6-1
30*853^1-1
32*853^2-1
36*853^1-1
38*853^1-1
42*853^94-1
44*853^19-1
48*853^68-1
50*853^1-1
54*853^1-1
56*853^6-1
60*853^26-1

The other k have trivial factors. With a conjectured k of 62, this conjecture is proven.

Riesel Base 694
 

Riesel Base 694
Conjectured k = 279
Covering Set = 5, 139
Trivial Factors k == 1 mod 3(3) and k == 1 mod 7(7) and k == 1 mod 11(11)

Found Primes: 141k's - File attached

Remaining k's: 2k's - Tested to n=25K
96*694^n-1
264*694^n-1

k=9 proven composite by partial algebraic factors

Trivial Factor Eliminations: 133k's

Base Released

Riesel base 743, k=32
Primes:
2*743^2-1
4*743^1-1
6*743^1-1
10*743^9-1
12*743^23-1
16*743^1-1
18*743^53-1
20*743^20-1
24*743^16-1
26*743^10-1
28*743^437-1
30*743^2-1

Trivial factors: k=8,22.
1 k's remain: 14*743^n-1

Base completed to 25K and released.

Riesel base 887, k=38.
Primes:
2*887^40-1
4*887^1-1
6*887^2-1
8*887^2-1
12*887^2-1
14*887^28-1
16*887^27-1
18*887^3-1
20*887^8-1
24*887^141-1
28*887^115-1
30*887^3-1
32*887^6-1
34*887^263-1
10*887^4107-1

2k's remain:
22*887^n-1
26*887^n-1

k=36 proven composite by partial algebraic factors.

Base completed to 25K and released.

serp bases 784, 785 and 788 are all tested to 50k and unreserving
results attached
to fit in the forum limit i had to compress using 7zip with customised settings(ultra wasnt good enough)
if you can't uncompress it i can reupload somewhere else

Riesel 526
 

Reserving Riesel 526 as new to n=25K

Riesel Base 550
 

Reserving Riesel Base 550 as new to n=25K

[quote=henryzz;212724]serp bases 784, 785 and 788 are all tested to 50k and unreserving
results attached
to fit in the forum limit i had to compress using 7zip with customised settings(ultra wasnt good enough)
if you can't uncompress it i can reupload somewhere else[/quote]

It doesn't appear that my laptop will download them. If I wasn't out of town, I'd look for the correct compression software and learn something about the settings but I don't have time right now.

Can you Email them to gbarnes017 at gmail dot com? That's the best way for medium and large-sized files.

Thanks.

S780 done to 100K. Base released.

R888 25K-50K complete, no primes.
Will continue it to 100K. Also reserving R800 to 100K.