(191*105^5045+1)/8 is (probable) prime!!!

S105 is proven!!!

S123 tested to n=8K (4K-8K)

nothing found, 3 remain

Reserve S113 and R123 to n=8K.

Reserve R67 to n=10K and R91 to n=8K.

Now, all 1k bases <= 128 are reserved to at least n=8K!!!

I will reserve all 2k and 3k bases after these 1k bases done to n=8K, including these bases:

S115 (3k), R70 (3k), R73 (2k), R85 (3k), R105 (3k), R118 (2k)

Also reserve R31 (for all remain k's) to n=12K after these 1k bases done to n=8K.

[QUOTE=sweety439;469842]Reserve R67 to n=10K and R91 to n=8K.

Now, all 1k bases <= 128 are reserved to at least n=8K!!!

I will reserve all 2k and 3k bases after these 1k bases done to n=8K, including these bases:

S115 (3k), R70 (3k), R73 (2k), R85 (3k), R105 (3k), R118 (2k)

Also reserve R31 (for all remain k's) to n=12K after these 1k bases done to n=8K.[/QUOTE]

(25*67^2829-1)/6 is (probable) prime!!!

R67 is proven!!!

(27*91^5048-1)/2 is (probable) prime!!!

R91 is proven!!!

[QUOTE=sweety439;469840]S123 tested to n=8K (4K-8K)

nothing found, 3 remain

Reserve S113 and R123 to n=8K.[/QUOTE]

S113 tested to n=8K (4K-8K)

nothing found, 1 remain

R123 tested to n=8K (4K-8K)

nothing found, 1 remain

The webpage for this thread:

Sierpinski conjectures: [URL="http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29"]http://www.mersennewiki.org/index.php/Sierpinski_problem_%28extended_definition%29[/URL]

Riesel conjectures: [URL="http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29"]http://www.mersennewiki.org/index.php/Riesel_problem_%28extended_definition%29[/URL]

(k*b^n+1)/gcd(k+1,b-1) has algebra factors if and only if k*b^n is either perfect odd power or of the form 4*m^4.

(k*b^n-1)/gcd(k-1,b-1) has algebra factors if and only if k*b^n is perfect power.

Sierpinski base 129
 

[CODE]
k,n
1,4
2,6
3,1
4,19
5,2
6,16796
7,1
8,1
9,15
10,1
11,2
12,1
13,1
[/CODE]

With CK=14, this base is proven.

Sierpinski base 132
 

[CODE]
k,n
1,4
2,2
3,1
4,2
5,1
6,5
7,3
8,2
9,2
10,1
11,1
12,2
[/CODE]

With CK=13, this base is proven.

Sierpinski base 133
 

[CODE]
k,n
1,1
2,1
3,2
4,5
5,2
6,3
7,1
8,7
9,1
10,4
11,4
12,1
13,3
14,2
15,1
16,1
17,2
18,2
19,806
20,1
21,1
22,1
23,?
24,2
25,1
26,1
27,8
28,6
29,1
30,5
31,1
32,6
33,2
34,1
35,2
36,1
37,2
38,43
39,1
40,2
41,8
42,4
43,12
44,1
45,8
46,4
47,1
48,18
49,1
50,6
51,?
52,1
53,2
54,1
55,3
56,3
57,174
58,10
[/CODE]

WIth CK=59, k=23 and 51 remain.