Reserving:

[CODE]
Base 22:

Sierpinski
22
484
[/CODE]

Base 22
 

[QUOTE=CedricVonck;95535]Reserving:

[CODE]
Base 22:

Sierpinski
22
484
[/CODE][/QUOTE]

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

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.

484=22*22

[QUOTE=CedricVonck;95538]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.[/QUOTE]

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

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

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.

[QUOTE=CedricVonck;95545]Ok thank you! :blush:
I sieved 22*2n+1 to 323 million with NewPgen from 0 to 1000000[/QUOTE]

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

Here are some results from phrot:
[code]
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)
[/code]
See if you can find anything below 128.

Oops, my fault.

Generalised Fermat Numbers
 

[QUOTE=axn1;95546]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.[/QUOTE]

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.

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?