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Old 2011-09-20, 04:40   #1
firejuggler
 
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Default k=43112609

oh well, wanna try this k, just for fun
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Old 2011-09-20, 04:56   #2
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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
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Old 2011-09-20, 06:12   #3
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I don't know if any of those divide any F or GF..and didn't find the tools to check
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Old 2011-09-20, 07:51   #4
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Quote:
Originally Posted by firejuggler View Post
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".
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Old 2011-09-20, 08:40   #5
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ah thanks.
it seems that none of them divide .

43112609*2^79751+1 is prime! Time : 7.363 sec. 24016 digits
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Old 2011-09-20, 11:39   #6
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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
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Old 2011-09-20, 17:43   #7
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RPS and NPLB are only for Riesel primes...that is the -1 side.
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Old 2011-09-20, 21:14   #8
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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
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Old 2011-09-20, 21:30   #9
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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
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Old 2011-09-20, 22:00   #10
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Quote:
Originally Posted by firejuggler View Post
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.
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Old 2011-09-20, 22:18   #11
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and since k==2 mod 3 there won't be twin prime

Last fiddled with by firejuggler on 2011-09-20 at 22:20
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