Hi Roman,
> I tryed to factorize 2^101-1, but Maxima can not do this.
The integer factorization code was recently improved.
The changes will be in the next release of Maxima.
In the meantime, you can download ifactor.lisp from
http://maxima.cvs.sourceforge.net/*checkout*/maxima/maxima/src/ifactor.lisp
and then load it into Maxima (compiling it first) by
:lisp (compile-file "ifactor.lisp")
:lisp (load "ifactor")
factor (2^101 - 1);
=> 7432339208719 341117531003194129
new function: ifactors (2^101 - 1);
=> [[7432339208719, 1], [341117531003194129, 1]]
FWIW
Robert Dodier