Algebra and base 9
 

Aiaia, such basic maths!! Why did I not spot that?

So all of these are trivial and the mooted Riesel base 9 is therefore proven.

Speaking of basic maths, tell me if I'm right or wrong:
[quote]Base 8:

Covering set [3,5,13] covering every 4 n. The corresponding Sierpinski number is 47, but it is not proven for the small fact that k=1 is known not to have small primes. (Think about it: 8^n+1= 2^3n+1[/quote]
For 2^n+1 to be prime n has to be 2^m for some m. If 2^n+1 has to have n be a power of 2, there's no way, in 2^3n+1 to find an n value that makes 3n a power of 2.

Did I miss something?

For base 16 Does this work sierpinski number =27473
It has multiple covering sets.

2158*16^n+1
2857*16^n+1
2908*16^n+1
3061*16^n+1
4885*16^n+1
5886*16^n+1
6348*16^n+1
6663*16^n+1
6712*16^n+1
7212*16^n+1
7258*16^n+1
7615*16^n+1
7651*16^n+1
7773*16^n+1
8025*16^n+1
10183*16^n+1
10425*16^n+1
10947*16^n+1
12243*16^n+1
12900*16^n+1
13023*16^n+1
13438*16^n+1
14026*16^n+1
14661*16^n+1
14910*16^n+1
15370*16^n+1
15441*16^n+1
16015*16^n+1
16390*16^n+1
16846*16^n+1
17118*16^n+1
17970*16^n+1
18598*16^n+1
18828*16^n+1
19122*16^n+1
19465*16^n+1
19575*16^n+1
19668*16^n+1
19687*16^n+1
19725*16^n+1
20212*16^n+1
20446*16^n+1
20452*16^n+1
21115*16^n+1
21181*16^n+1
21436*16^n+1
21720*16^n+1
21943*16^n+1
22458*16^n+1
22747*16^n+1
23451*16^n+1
23682*16^n+1
24262*16^n+1
24505*16^n+1
24582*16^n+1
24790*16^n+1
26017*16^n+1
26215*16^n+1
26892*16^n+1
26977*16^n+1

These have been tested to n=4000. (under 27473 only)

Base 16 Sierpinski
 

Extended above to 4400. The following primes were found. Stopping here. The numbers are free to take.:smile:

22747*2^16432+1 is prime!
12900*2^16508+1 is prime!

Taking the following numbers:

2158*16^n+1
2857*16^n+1
2908*16^n+1
3061*16^n+1
4885*16^n+1

26977*2^20204+1 is prime! Time: 2.663 sec.

so status is
[CODE]2158*16^n+1 jasong
2857*16^n+1 jasong
2908*16^n+1 jasong
3061*16^n+1 jasong
4885*16^n+1 jasong
5886*16^n+1 tnerual
6348*16^n+1
6663*16^n+1
6712*16^n+1
7212*16^n+1
7258*16^n+1
7615*16^n+1
7651*16^n+1
7773*16^n+1
8025*16^n+1
10183*16^n+1
10425*16^n+1
10947*16^n+1
12243*16^n+1
13023*16^n+1
13438*16^n+1
14026*16^n+1
14661*16^n+1
14910*16^n+1
15370*16^n+1
15441*16^n+1
16015*16^n+1
16390*16^n+1
16846*16^n+1
17118*16^n+1
17970*16^n+1
18598*16^n+1
18828*16^n+1
19122*16^n+1
19465*16^n+1
19575*16^n+1
19668*16^n+1
19687*16^n+1
19725*16^n+1
20212*16^n+1
20446*16^n+1
20452*16^n+1
21115*16^n+1
21181*16^n+1
21436*16^n+1
21720*16^n+1
21943*16^n+1
22458*16^n+1
23451*16^n+1
23682*16^n+1
24262*16^n+1
24505*16^n+1
24582*16^n+1
24790*16^n+1
26017*16^n+1
26215*16^n+1
26892*16^n+1
[/CODE]

Base 16 Sierpinski
 

[QUOTE=Citrix;96821]For base 16 Does this work sierpinski number =27473
It has multiple covering sets.

[/QUOTE]

Citrix, I had considered 27473 with covering set [7,13,17,241] but sadly it is a trivial result (all n divided by 3) as the results for n=1..6 show

1 3^2*13^2*17^2
2 3*7*179*1871
3 3*17*23^2*43*97
4 3^2*11*13*1398967
5 3*7*17*2113*38189
6 3*241*401*1589803

So I will stick to my guns and I think 66741 is the smallest. The good news is that the work you have carried out has not gone to waste, you just need to check more k !!

5886*2^108040+1 is prime! Time: 66.218 sec.

so status for base 16, sierpinski is ( with robert's remark)
[CODE]2158*16^n+1 jasong
2857*16^n+1 jasong
2908*16^n+1 jasong
3061*16^n+1 jasong
4885*16^n+1 jasong
6348*16^n+1
6663*16^n+1
6712*16^n+1
7212*16^n+1
7258*16^n+1
7615*16^n+1
7651*16^n+1
7773*16^n+1
8025*16^n+1
10183*16^n+1
10425*16^n+1
10947*16^n+1
12243*16^n+1
13023*16^n+1
13438*16^n+1
14026*16^n+1
14661*16^n+1
14910*16^n+1
15370*16^n+1
15441*16^n+1
16015*16^n+1
16390*16^n+1
16846*16^n+1
17118*16^n+1
17970*16^n+1
18598*16^n+1
18828*16^n+1
19122*16^n+1
19465*16^n+1
19575*16^n+1
19668*16^n+1
19687*16^n+1
19725*16^n+1
20212*16^n+1
20446*16^n+1
20452*16^n+1
21115*16^n+1
21181*16^n+1
21436*16^n+1
21720*16^n+1
21943*16^n+1
22458*16^n+1
23451*16^n+1
23682*16^n+1
24262*16^n+1
24505*16^n+1
24582*16^n+1
24790*16^n+1
26017*16^n+1
26215*16^n+1
26892*16^n+1
and 27473 to 66740
[/CODE]

i will take the base 16 sierpinski from 27473 to 66740 ... :sick:

[QUOTE=tnerual;96946]i will take the base 16 sierpinski from 27473 to 66740 ... :sick:[/QUOTE]

i'm not able to manage it.

if someone has an app running under windows (or command line), able to do the job i will be happy :smile:

the app has to do this:
1. test all k for n=2
2. remove all k with primes found in 1.
3. test all remaining k for n=3
4. remove all k with primes found in 3.

and so on.

i am totaly unable to program anything and excel, supposed to be my friend is not in reality ...

maybe a programmer guru can do that ... it will help a lot of people (at least one :geek: )

[QUOTE=tnerual;96996]i'm not able to manage it.

if someone has an app running under windows (or command line), able to do the job i will be happy :smile:

the app has to do this:
1. test all k for n=2
2. remove all k with primes found in 1.
3. test all remaining k for n=3
4. remove all k with primes found in 3.

and so on.

i am totaly unable to program anything and excel, supposed to be my friend is not in reality ...

maybe a programmer guru can do that ... it will help a lot of people (at least one :geek: )[/QUOTE]
You're worrying for nothing, dude. 16 is 2^4, and LLR notices this. Just sieve in base-16 and send it directly to LLR. When the LLR program sees base-16, it changes the base to 2 and multiplies the n-value by 4. No work needs to be done on the file, LLR is smart enough to figure it out on it's own.

Edit: By the way guys:

2857*16^5478+1 is prime
2158*16^10906+1 is prime
4885 tested to n=50,000(base-16) no primes
3061 tested to n=50000(base-16) no primes
2908 tested to n=38000(base-16) no primes

I'm unreserving all my numbers.

Thanks.