# prime powers and primes

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
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