Sierpinski/ Riesel bases 6 to 18

[robert44444uk]

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.

[jasong]

Speaking of basic maths, tell me if I'm right or wrong:

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

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?

[Citrix]

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)

[Citrix]

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

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

[jasong]

Taking the following numbers:

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

[tnerual]

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

so status is

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

[robert44444uk]

Originally Posted by Citrix

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

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 !!

[tnerual]

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

so status for base 16, sierpinski is ( with robert's remark)

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

[tnerual]

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

[tnerual]

Originally Posted by tnerual

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

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

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 )

[jasong]

Originally Posted by tnerual

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

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 )

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.