One way of telling the story is this: as we keep traversing ever larger numbers, we can always find a pair of primes whose distance is less than 70 million. Th

One way of telling the story is this: as we keep traversing ever larger numbers, we can always find a pair of primes whose distance is less than 70 million. The twin primes conjecture holy grail is this: no matter how big we go, we can always find a pair of primes whose distance is the minimal possible, i.e. 2. So as sparse as these pairs become in the limit according to the prime number theorem, the likelihood of finding them remains always positive.