  We investigate the duality between the Nekrasov function and the quantized
Seiberg-Witten prepotential, first guessed in [1] and further elaborated in [2]
and [3]. We concentrate on providing more thorough checks than the ones
presented in [3] and do not discuss the motivation and historical context of
this duality. The check of the conjecture up to $o (\hbar^6, \ln (\Lambda))$ is
done by hands for arbitrary $N$ (explicit formulas are presented). Moreover,
details of the calculation that are essential for the computerization of the
check are worked out. This allows us to test the conjecture up to $\hbar^6$ and
up to higher powers of $\Lambda$ for $N = 2,3,4$. Only the case of pure SU(N)
gauge theory is considered.
