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Topic: TWIN PRIME REVISED
Replies: 13   Last Post: Dec 12, 2017 10:53 PM

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eestath

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

proof

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
p
+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
+2
( both primes)
then

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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