Sierpinski/ Riesel bases 6 to 18

[ValerieVonck]

Reserving:

Base 22:

Sierpinski
22
484

[robert44444uk]

Originally Posted by CedricVonck

Reserving:

Base 22:

Sierpinski
22
484

Cedric, you only need to check one of these, the other automatically follows

[ValerieVonck]

Robert,

I cannot follow anymore.
Are you saying that is only necessary to test 1 number of this set??
Please explain a bit.

Thank you.

[S485122]

484=22*22

[robert44444uk]

Originally Posted by CedricVonck

Robert,

I cannot follow anymore.
Are you saying that is only necessary to test 1 number of this set??
Please explain a bit.

Thank you.

S485122 has said it.

Looking at k*b^n+1, where k and b are the same = A, then A*A^n+1 is the same as A^2*A^(n-1)+1 (also A^3*A^(n-2)+1)......

For example 484*22^n+1 is the same as 22^2*22^n+1 = 22*22^(n+1)+1, therefore if you find a prime for k=22, then you automatically find a prime for 484, it will just have an n value one smaller. It is important to not test both because otherwise you ended up with double testing

[ValerieVonck]

Ok thank you!
I sieved 22*22^n+1 to 323 million with NewPgen from 0 to 1000000

[axn]

If you are looking for primes of the form 22^n+1, then all the n's must be of the form 2^m, no? Such a series is expected to have only a finite number of primes. I _really_ doubt if you would find any primes other than 23 (n=1) in this series.

[axn]

Originally Posted by CedricVonck

Ok thank you!
I sieved 22*2n+1 to 323 million with NewPgen from 0 to 1000000

It should be 22*22^n+1, not 2. Anyway, no need to sieve. Just look for n=2^m.

Here are some results from phrot:

1*22^128+1 [-886614,-2341416,2094222,1285347] is composite LLR64=38BEBAE0096A42D9. (e=0.03348 (0.043388~2.47225e-16@1.154) t=0.00s)
1*22^256+1 [-1215165,-2572984,594225,1500360] is composite LLR64=1C5B026ED89F9F69. (e=0.05851 (0.0695243~3.05492e-16@0.885) t=0.02s)
1*22^512+1 [864935,1437214,-1120667,-2517486] is composite LLR64=45172DB5C2379217. (e=0.07143 (0.109179~2.6498e-16@0.990) t=0.03s)
1*22^1024+1 [-97740,192575,2458602,2271844] is composite LLR64=6C722426EC90FF26. (e=0.12500 (0.170124~3.28705e-16@0.985) t=0.14s)
1*22^2048+1 [2527460,-1546581,-2527633,-2057527] is composite LLR64=39AB09F2B5303ED8. (e=0.21428 (0.263517~3.98438e-16@1.156) t=0.58s)
1*22^4096+1 [-20646,94236,-26597,45123] is composite LLR64=D160E108FD94EEF3. (e=0.00084 (0.00124097~4.77784e-16@1.032) t=3.13s)
1*22^8192+1 [47594,112255,-93362,-107811] is composite LLR64=60294051C46B18BE. (e=0.00141 (0.00186038~5.67875e-16@1.245) t=13.38s)
1*22^16384+1 [-9782,3764,-6112,75344] is composite LLR64=96B850129A9FDC51. (e=0.00195 (0.00278033~5.56052e-16@0.995) t=56.87s)
1*22^32768+1 [-111027,28678,-12860,-70925] is composite LLR64=54389F735CDF6934. (e=0.00304 (0.00414345~6.11658e-16@0.948) t=241.38s)

See if you can find anything below 128.

[ValerieVonck]

Oops, my fault.

[robert44444uk]

Originally Posted by axn1

If you are looking for primes of the form 22^n+1, then all the n's must be of the form 2^m, no? Such a series is expected to have only a finite number of primes. I _really_ doubt if you would find any primes other than 23 (n=1) in this series.

Is there a case for excluding GFN's? Probably not, as such numbers might produce primes, but we should accept that such bases are going to give us problems.

[Xentar]

Just found in the prime database, that
18 * 14^70119+1
is prime.
Can I use this in any way for
18 * 18^n +1
?

Or, what have I search for, to make the work easier?