With the exception of $4$, every number located between twin primes is divisible by $6$.
This one is obvious, but are there any other properties that can be ascribed to such numbers?
A property may be ascribed either to each number individually or to the entire sequence.
For example, consider the amount of prime factors of such numbers:
- Is there any known restriction on this amount per each number?
- Is there any known restriction on this amount as a function of the sequence-index?
The context in which I am asking this question:
What attempts have been made towards proving that there are infinitely many pairs of twin primes, by proving that there are infinitely many numbers located between twin primes?