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Old 2006-01-11, 16:11   #1
Greenbank
 
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Jul 2005

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*** Definition (by Dougy)

For natural numbers k,n, with k < 2^n, if the following are all primes:

k*2^n+1
k*2^n-1
k*2^(n+1)+1
k*2^(n+1)-1
2^n+k
2^n-k
2^(n+1)+k
2^(n+1)-k

then k*2^n+1 is called an octoproth.

It can be shown that if k*2^n+1 is an octoproth then k = 15 (mod 30) and if n != 1 (mod 3) then k = 105 mod 210

Last fiddled with by Greenbank on 2006-01-11 at 16:43
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