Thread: Octoproths
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Old 2005-04-16, 06:50   #51
Dougy
 
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Aug 2004
Melbourne, Australia

23·19 Posts
Lightbulb Some maths

If k*2^n+1 is an octoproth then

k = 1 mod 2. If k is even then 2^(n+1) + k is divisible by 2.

k = 0 mod 3. If k = 1 mod 3 then either 3 divides k*2^n+1 or k*2^(n+1)+1. Similarly for k = 2 mod 3

k = 0 mod 5.

k = 0 mod 7 or (n = 1 mod 3 and k = +/- 1 mod 7).

I can't make any other useful criteria from any other primes. Does anybody know of other goodies like this?
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