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Posts: 141
Registered: 9/2/05
Posted: Jun 16, 2009 1:51 PM
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There are infinitely many primes p such that p + 2 is also prime.


We assume that the biggest pair is p and p+2. We can know create the
function :

L(n,p)=flour{ n(1/p(p+2))}

Where p+2 is the largest asummed prime number of the pair p and p+2
and n is the a positive integer greater than p+2.
The function L gives the number of integers that have as factor p and
+2(up to n).

if p and p+2 is the biggest pair then L >0.

if we asume that there are infinite prime numbers of the form p and p
( both primes)

lim(p-->oo)( L(n,p))=flour{ n(1/p(p+2))})=0.

that contrudicts the assumption that L>0 allways. So there is a finite
set of primes of the form p and p+2 both primes.

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