Deterministic Prime Construction [duplicate]

Possible Duplicate:
Finding a prime greater than a given bound

Question

Does there exist

• a polynomial $q$
• and a deterministic polynomial time algorithm $A$

such that for all sufficiently large $n$, we have:

$A(n)$ outputs a prime $p$ s.t. $n \leq p \leq q(n)$. (Note $n$ is stored in binary, so $A$ must run in $poly(\log n)$ time.)

Context

Suppose that for some derandomization task we need to be able to construct primes. This rules out the "guess a random number + check" approach since we can't use randomness.