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



eestath
Posts:
141
Registered:
9/2/05


TWIN PRIME REVISED
Posted:
Jun 16, 2009 1:51 PM


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.



