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 2011-09-20, 04:40 #1 firejuggler     Apr 2010 Over the rainbow 2·1,217 Posts k=43112609 oh well, wanna try this k, just for fun
 2011-09-20, 04:56 #2 firejuggler     Apr 2010 Over the rainbow 1001100000102 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 2011-09-20 at 05:54
 2011-09-20, 06:12 #3 firejuggler     Apr 2010 Over the rainbow 2·1,217 Posts I don't know if any of those divide any F or GF..and didn't find the tools to check
2011-09-20, 07:51   #4
kar_bon

Mar 2006
Germany

1011001000102 Posts

Quote:
 Originally Posted by firejuggler I don't know if any of those divide any F or GF..and didn't find the tools to check
Try pfgw with option "-go" or "-gxo".

 2011-09-20, 08:40 #5 firejuggler     Apr 2010 Over the rainbow 2·1,217 Posts ah thanks. it seems that none of them divide . 43112609*2^79751+1 is prime! Time : 7.363 sec. 24016 digits
 2011-09-20, 11:39 #6 firejuggler     Apr 2010 Over the rainbow 2·1,217 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 2011-09-20 at 11:43
 2011-09-20, 17:43 #7 gd_barnes     May 2007 Kansas; USA 3·3,407 Posts RPS and NPLB are only for Riesel primes...that is the -1 side.
 2011-09-20, 21:14 #8 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts 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 Edit: no twins here, either -3 or +1. Last fiddled with by Mini-Geek on 2011-09-20 at 21:38
 2011-09-20, 21:30 #9 firejuggler     Apr 2010 Over the rainbow 1001100000102 Posts I also checked the counterpart of every +1 prime. No -1 is prime Last fiddled with by firejuggler on 2011-09-20 at 21:31
2011-09-20, 22:00   #10
kar_bon

Mar 2006
Germany

2×3×52×19 Posts

Quote:
 Originally Posted by firejuggler I also checked the counterpart of every +1 prime. No -1 is prime
k*2^n-1 and k*2^n+1 (k>1) both primes (so twins) -> k == 0 mod 3.

 2011-09-20, 22:18 #11 firejuggler     Apr 2010 Over the rainbow 98216 Posts and since k==2 mod 3 there won't be twin prime Last fiddled with by firejuggler on 2011-09-20 at 22:20