I'm not a mathematician, but this is an interesting subject to me.
Does this imply a certain density to prime numbers? And given this new information, does it mean that it could be less computationally hard to find or verify primes?
Does this imply a certain density to prime numbers? And given this new information, does it mean that it could be less computationally hard to find or verify primes?
Having said that, the primes do have a known density, given by the Prime Number Theorem [1]. This theorem states that the number of primes less then x is x/ln(x), as x approaches infinity.
What this theorem says is that no matter how large the numbers get, no matter how sparsely the primes are spread out, on average, there will always be pairs of primes that are relatively close (within 600 of each other)