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How close is too close?

if \rm\:|p-q| < n^{1/3},\:
then n can factored in polynomial time using fermat algorithm:

def fermatfactor(N):
  if N <= 0: return [N]
  if is_even(N): return [2,N/2]
  a = ceil(sqrt(N))
  while not is_square(a^2-N):
    a = a + 1
  b = sqrt(a^2-N)
  return [a - b,a + b]

Instructions

This folders contains two public keys:

veryclosepq.pem
notsoclosepq.pem

Use the provided algorithm to factor n.

A detailed explanation of this method can be found on Daniel's Bernstein website, or John D. Cooks's.