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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
by possibilistic 13y ago
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?
- boyter 13y agoI would be curious to know what impact this would have on primecoin which appears to have gained a lot of traction over the last few months.
- gizmo686 13y agoNot directly. This says that at any point on the number line, if you go sufficiently farther down the number line, you can always find 2 primes whose difference is no more than 600. It is possible that the distance between such groups gets arbitrarily large (at an arbitrarily fast rate) as you go down the number line. 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. [1]http://en.wikipedia.org/wiki/Prime_number_theorem http://en.wikipedia.org/wiki/Prime_number_theorem
- iclelland 13y agoThe overall density of primes is known, and decreases continuously as the numbers get larger (See http://en.wikipedia.org/wiki/Prime_number_theorem http://en.wikipedia.org/wiki/Prime_number_theorem) 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)