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let be a prime p and nother prime q

would it be true that for the prime powers of p $ p^{m} $ and 'm' positive integer would be another prime near q

so what would be the distance $ |p^{m}-q| $

my idea is to know if for every prime powers there is close another prime for example

$ 2^{4}=16 $ there is a prime 17 very near

$ 17^{3}= 4913 $ but 4919 is a prime , and $5^{4}=625 $ but 631 is prime

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This depends rather crucially on how you define "near $q$", and unless you are a bit more precise on this score, it is going to be hard to give a useful answer. –  Old John Nov 10 '13 at 11:25
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What counts as "near"? –  Hagen von Eitzen Nov 10 '13 at 11:25
    
This could be somewhat related: math.stackexchange.com/questions/288439/… –  Sebastian Nov 10 '13 at 11:45
    
the distance between $ |p^{m}-q| $ with p and q primes could be less than 10 or 100 :) or 1000 see my examples –  Jose Garcia Nov 10 '13 at 13:45

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