Twin primes are pairs of primes which differ by two. The first twin primes are {3,5}, {5,7}, {11,13} and {17,19}. It has been conjectured (but never proven) that there are infinitely many twin primes. If the probability of a random integer n and the integer n+2 being prime were statistically independent events, then it would follow from the prime number theorem that there are about n/(log n)2 twin primes less than or equal to n.

Please prove or disprove this conjecture. Thank you.