20110920, 04:40  #1 
Apr 2010
Over the rainbow
2^{4}·3·7^{2} Posts 
k=43112609
oh well, wanna try this k, just for fun

20110920, 04:56  #2 
Apr 2010
Over the rainbow
2^{4}×3×7^{2} Posts 
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 Last fiddled with by firejuggler on 20110920 at 05:54 
20110920, 06:12  #3 
Apr 2010
Over the rainbow
2^{4}·3·7^{2} Posts 
I don't know if any of those divide any F or GF..and didn't find the tools to check

20110920, 07:51  #4 
Mar 2006
Germany
2,801 Posts 

20110920, 08:40  #5 
Apr 2010
Over the rainbow
4460_{8} Posts 
ah thanks.
it seems that none of them divide . 43112609*2^79751+1 is prime! Time : 7.363 sec. 24016 digits 
20110920, 11:39  #6 
Apr 2010
Over the rainbow
2^{4}×3×7^{2} Posts 
n tested up to 100k, no further prime.
LLR test take around 15 seconds (up to 18) each at 100k Last fiddled with by firejuggler on 20110920 at 11:43 
20110920, 17:43  #7 
May 2007
Kansas; USA
3×11×307 Posts 
RPS and NPLB are only for Riesel primes...that is the 1 side.

20110920, 21:14  #8 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
I searched 43112609*b^n1 for b <= 10 and n <= 10000. This is all the primes: (includes duplicates, e.g. 2^16 and 4^8)
Code:
43112609*10^11 43112609*2^161 43112609*2^561 43112609*2^1241 43112609*2^2681 43112609*2^2721 43112609*4^81 43112609*4^281 43112609*4^621 43112609*4^1341 43112609*4^1361 43112609*4^6581 43112609*4^8021 43112609*4^8181 43112609*6^31 43112609*6^851 43112609*6^7331 43112609*6^8311 43112609*10^811 43112609*10^2591 43112609*10^9271 43112609*2^13161 43112609*2^16041 43112609*2^16361 43112609*6^73951 43112609*10^30191 Last fiddled with by MiniGeek on 20110920 at 21:38 
20110920, 21:30  #9 
Apr 2010
Over the rainbow
2^{4}×3×7^{2} Posts 
I also checked the counterpart of every +1 prime.
No 1 is prime Last fiddled with by firejuggler on 20110920 at 21:31 
20110920, 22:00  #10 
Mar 2006
Germany
2,801 Posts 

20110920, 22:18  #11 
Apr 2010
Over the rainbow
4460_{8} Posts 
and since k==2 mod 3 there won't be twin prime
Last fiddled with by firejuggler on 20110920 at 22:20 