Sierpinski/ Riesel bases 6 to 18

[robert44444uk]

Originally Posted by CedricVonck

Ok relaasing 1343*16^n-1.

LLR seemed to test this number as a 1343*2^n-1.

Not the end of the world, but it sounds like you are testing too many numbers, as you only need check every 4th n. As in 1343*(2^4)^n-1

You might want to try pfgw. It is very flexible and you can check all sorts of combinations of numbers. It is totally tested software, and not too bad to use once you get used to it.

[robert44444uk]

Just to prove this is not so obvious an exercise. I discovered for base 26 a lower riesel series which is more complex than the simple ones I usually check for. It proves that, although every number, save the b=2^n-1 ones, has a covering set with a repeat of 12 or less, this does not always give rise to the smallest k.

Sierpinski 221 [3,19,37,7] repeating every 12n. Remaining candidates at n=2000 are 32,65,155,217

Riesel 149 [3,7,17,31,37] repeating every 24n. Remaining candidates at n=2000 are 32 and 115.

[robert44444uk]

Originally Posted by tnerual

so actual status is:

Base 20: 
?

See message 27

[robert44444uk]

Originally Posted by axn1

Personally, I like to exclude them, since they are not prime "trivially" (for some weird definition of trivial ). Plus there is a neat symmetry, since the corresponding -1 series is also excluded due to triviality.

Anyway, FWIW, couple more tests:

1*22^65536+1 [86924,-94019,-53914,4292] is composite LLR64=025A0D6038FFD624. (e=0.00496 (0.00615895~7.06466e-16@1.019) t=1009.07s)
1*22^131072+1 [-45196,-45619,-74943,30011] is composite LLR64=F8D5A92E929D694B. (e=0.00694 (0.00913339~6.99073e-16@0.998) t=4347.90s)

Currently testing the next one. After that, I'll call it quits (maybe I should've sieved these, hmmm... )

Trivials are those which can never be prime. The values we are looking at could be prime, so not so trivial.

[tnerual]

for sierpinski base 11, i unreserve the 2 number i had:

416*11^n+1 tested up to 416*11^7801+1, no prime
958*11^n+1 tested up to 958*11^57904+1, no prime ...

[Xentar]

Eh.. new status:

18 * 18 ^ n + 1
stopped testing at n=170623

122
testing, n=57358

381
not tested yet

still no primes :( something wrong here?

[thommy]

Originally Posted by Xentar

18 * 18 ^ n + 1
stopped testing at n=170623

As Phil pointed out in http://www.mersenneforum.org/showpos...64&postcount=5
18 * 18 ^ n + 1=18^m+1 with m=n+1. 18^m+1 can only be prime if m=2^k for some k. There is no use in testing other values of m.

[Xentar]

Originally Posted by thommy

As Phil pointed out in http://www.mersenneforum.org/showpos...64&postcount=5
18 * 18 ^ n + 1=18^m+1 with m=n+1. 18^m+1 can only be prime if m=2^k for some k. There is no use in testing other values of m.

Thats the reason, I stopped testing :D

[jasong]

tested to 4*9^165552-1. unreserving.

Here's the residuals and sieve file.(Darn, I just discovered I can only upload 1 file at once. If you want either file, you can PM me.)

Edit by Max (8/30/09): cleaned up attachment (no longer needed since Riesel base 9 was proved a while back)

[Xentar]

381*18^24108+1 is a probable prime.

So, I still have
k = 122 base 18

[geoff]

Originally Posted by robert44444uk

Base 9:

Covering set every 6n for [5,7,13,73]. Alternative covering set every 8 n for [5,41,17,193]. Lowest mooted Sierpinski is 2344 (k=439 is not Sierpinski because the k is also trivial). Lowest conjectured Riesel is 74, so should be easy to prove, but 4,16,36,64 are proving pesky. Note 16 and 64 are subsets of 4.

4*9^n-1 = (2*3^n-1)(2*3^n+1), so there are no primes to be found here.

Same applies to 16,36,64.