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No. The average size of a prime gap around numbers of size N is ln(N).

http://en.wikipedia.org/wiki/Prime_number_theorem

A rough analogy of this prime gaps work is the following. Imagine that you throw infinitely many darts at a dartboard. Before you throw, draw a bullseye around the center, as small as you want. Then you will miss plenty often, but infinitely many of the darts will hit the bullseye.




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