k=43112609
 

oh well, wanna try this k, just for fun

43112609*2^63 + 1 is prime! (a = 3) [27 digits]

43112609*2^63 + 1 is prime! (verification : a = 5) [27 digits]

43112609*2^83 + 1 is prime! (a = 3) [33 digits]

43112609*2^83 + 1 is prime! (verification : a = 5) [33 digits]

43112609*2^219 + 1 is prime! (a = 3) [74 digits]

43112609*2^219 + 1 is prime! (verification : a = 5) [74 digits]

43112609*2^297 + 1 is prime! (a = 3) [98 digits]

43112609*2^297 + 1 is prime! (verification : a = 11) [98 digits]

43112609*2^1167 + 1 is prime! (a = 3) [359 digits]

43112609*2^1167 + 1 is prime! (verification : a = 5) [359 digits]

43112609*2^2351 + 1 is prime! (a = 3) [716 digits]

43112609*2^2351 + 1 is prime! (verification : a = 5) [716 digits]

43112609*2^2567 + 1 is prime! (a = 3) [781 digits]

43112609*2^2567 + 1 is prime! (verification : a = 5) [781 digits]

43112609*2^2739 + 1 is prime! (a = 3) [833 digits]

43112609*2^2739 + 1 is prime! (verification : a = 5) [833 digits]

43112609*2^3983 + 1 is prime! (a = 3) [1207 digits]

43112609*2^3983 + 1 is prime! (verification : a = 5) [1207 digits]

43112609*2^4191 + 1 is prime! (a = 3) [1270 digits]

43112609*2^4191 + 1 is prime! (verification : a = 5) [1270 digits]

43112609*2^5377 + 1 is prime! (a = 3) [1627 digits]

43112609*2^5377 + 1 is prime! (verification : a = 7) [1627 digits]

43112609*2^7863 + 1 is prime! (a = 3) [2375 digits]

43112609*2^7863 + 1 is prime! (verification : a = 5) [2375 digits]

43112609*2^11567 + 1 is prime! (a = 3) [3490 digits]

43112609*2^11567 + 1 is prime! (verification : a = 5) [3490 digits]

43112609*2^18707 + 1 is prime! (a = 3) [5640 digits]

43112609*2^18707 + 1 is prime! (verification : a = 5) [5640 digits]

43112609*2^45459+1 is prime! Time : 3.940 sec. 13693 digits

43112609*2^64081+1 is prime! Time : 5.383 sec. 19298 digits

43112609*2^64259+1 is prime! Time : 6.118 sec. 19352 digits

I don't know if any of those divide any F or GF..and didn't find the tools to check

[QUOTE=firejuggler;272116]I don't know if any of those divide any F or GF..and didn't find the tools to check[/QUOTE]

Try pfgw with option "-go" or "-gxo".

ah thanks.
it seems that none of them divide .

43112609*2^79751+1 is prime! Time : 7.363 sec. 24016 digits

n tested up to 100k, no further prime.
LLR test take around 15 seconds (up to 18) each at 100k

RPS and NPLB are only for Riesel primes...that is the -1 side.

I searched 43112609*b^n-1 for b <= 10 and n <= 10000. This is all the primes: (includes duplicates, e.g. 2^16 and 4^8)
[CODE]43112609*10^1-1
43112609*2^16-1
43112609*2^56-1
43112609*2^124-1
43112609*2^268-1
43112609*2^272-1
43112609*4^8-1
43112609*4^28-1
43112609*4^62-1
43112609*4^134-1
43112609*4^136-1
43112609*4^658-1
43112609*4^802-1
43112609*4^818-1
43112609*6^3-1
43112609*6^85-1
43112609*6^733-1
43112609*6^831-1
43112609*10^81-1
43112609*10^259-1
43112609*10^927-1
43112609*2^1316-1
43112609*2^1604-1
43112609*2^1636-1
43112609*6^7395-1
43112609*10^3019-1
[/CODE]
Edit: no twins here, either -3 or +1.

I also checked the counterpart of every +1 prime.
No -1 is prime

[QUOTE=firejuggler;272197]I also checked the counterpart of every +1 prime.
No -1 is prime[/QUOTE]

k*2^n-1 and k*2^n+1 (k>1) both primes (so twins) -> k == 0 mod 3.

and since k==2 mod 3 there won't be twin prime

[QUOTE=firejuggler;272211]and since k==2 mod 3 there won't be twin prime[/QUOTE]

There could be with -3/-1 or +3/+1, just not with -1/+1.

n checked upto 200k, still no new prime

FFT @20k, each test take 70 second, time to sieve a bit further.