  For a one-dimensional chain of four nuclear spins (1/2) and taking into
account first and second neighbor interactions among the spin system, we make
the numerical simulation of Shor prime factorization algorithm of the integer
number N=4 to study the influence of the second neighbor interaction on the
performance of this algorithm. It is shown that the optimum Rabi's frequency to
control the non-resonant effects is dominated by the second neighbor
interaction coupling parameter ($J'$), and that a good Shor quantum
factorization is achieved for a ratio of second to first coupling constant of
$J'/J\ge 0.04$.
