Reserving R251.

Riesel base 251, conjectured k = 8, proven
Primes:
2*251^2-1
4*251^271-1

k=6 removed by trivial factors
k=8 is proven composite (all numbers are divisible by 3 or 7)

Sierpinski base 422
 

Primes found:

[code]
2*422^3+1
3*422^2+1
4*422^2634+1
5*422^1+1
6*422^32+1
7*422^2+1
9*422^105+1
10*422^2978+1
11*422^1+1
12*422^394+1
14*422^5+1
15*422^12+1
18*422^13+1
19*422^7302+1
20*422^355+1
21*422^1+1
23*422^989+1
24*422^3+1
25*422^4+1
26*422^1+1
27*422^2+1
28*422^2+1
29*422^1+1
30*422^2+1
32*422^179+1
32*422^179+1
33*422^1302+1
34*422^946+1
35*422^1+1
36*422^1+1
37*422^13020+1
38*422^45+1
39*422^5+1
40*422^286+1
41*422^4319+1
42*422^4+1
43*422^2+1
44*422^223+1
45*422^3+1
[/code]

Remaining k at n=25000:
[code]
8*422^n+1
13*422^n+1
16*422^n+1
17*422^n+1
22*422^n+1
31*422^n+1
[/code]

I am releasing this base. This is just a nasty base because a large percentage of k remain. Does anyone know which conjectures (to this point) have the largest ratio of k remaining to conjectured k?

Riesel base 321 (conjectured k=22)
Primes:
2*321^1-1
4*321^1-1
10*321^1-1
12*321^1-1
14*321^1-1
18*321^4-1
20*321^1406-1

k=6 and k=16 removed by trivial factors.

Remaining k=8 tested to 25K with no primes, I'll reserve it to 100K.

[quote=unconnected;206059]Remaining k=8 tested to 25K with no primes, I'll reserve it to 100K.[/quote]
All n == 0 mod 3 can be eliminated since 8 is a cube.

[tex]8*321^n-1=2^3*321^{3m}-1=(2*321^m)^3-1[/tex]
And a sum or difference of cubes (1 is also a cube) has algebraic factors: [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

This eliminated ~100 candidates after sieving to 10G, not so bad. I wrote bash-script to do this, is there an easier way?

[quote=unconnected;206102]This eliminated ~100 candidates after sieving to 10G, not so bad. I wrote bash-script to do this, is there an easier way?[/quote]
Well, I made this Perl script a while ago: [url]http://www.mersenneforum.org/showthread.php?p=199328#post199328[/url]
It's probably a bit more complex and flexible (and so harder to use) than you need, but it works. :smile:

Reserving the following bases from my former k=2 search. I had already done some work on all of them to n=5K or 10K and have recently been moving them up towards n=25K. I'll post a status separately.

R383
S365
S461
S467

S461 is complete to n=25K; only k=2 remains; base released.
S467 is complete to n=25K; k=2 & 4 remain; base released.

Riesel Base 422
 

Primes found:

[code]
2*422^540-1
3*422^190-1
4*422^21737-1
5*422^2-1
6*422^1-1
7*422^1-1
8*422^2944-1
9*422^1-1
10*422^1-1
12*422^8-1
15*422^1-1
16*422^247-1
17*422^6-1
18*422^11-1
19*422^1-1
20*422^6-1
21*422^1-1
22*422^1-1
23*422^5568-1
24*422^4-1
25*422^9-1
26*422^642-1
27*422^1-1
28*422^3-1
30*422^1-1
31*422^33-1
32*422^6-1
33*422^11-1
34*422^1-1
35*422^2-1
36*422^37-1
38*422^2-1
39*422^21-1
40*422^1-1
41*422^22802-1
42*422^48-1
43*422^11-1
44*422^4-1
45*422^43-1
[/code]

k=1 has trivial factors.

These k remain:

[code]
11*422^n-1
13*422^n-1
14*422^n-1
29*422^n-1
37*422^n-1
[/code]

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

S365 is complete to n=25K; k=2 & 176 remain; base released.