Let p and q two distinct odd prime numbers.

p and q are twin primes if and only if (p+q)/(p-q) is integer.

--> trivial

<-- A= (p+q)/(p-q) Integer then A+1 is integer A+1=2p/(p-q)let r prime r | (p-q) then r | 2p then r | p+q then r | 2q GCD(p,q)=1 then r=2then p-q=2^kif 4 | (p-q) implies 4 | 2p and 4 | 2q y then 2 | p absurditythen p-q=2

Sincerely

Sebastian Martin Ruiz

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