  We consider binomial Thue equations of type $x^n-my^n=\pm 1$ in $x,y\in Z$.
Optimizing the method of Peth\H o we perform an extensive calculation by a high
performance computer to determine all solutions with $\max(|x|,|y|)<10^{500}$
of binomial Thue equations for $m<10^7$ for exponents
$n=3,4,5,7,11,13,17,19,23,29$.
