  In this work initial numbers and repunit numbers have been studied. All
numbers have been considered in a decimal notation. The problem of simplicity
of initial numbers has been studied. Interesting properties of numbers repunit
are proved:
  $gcd(R_a, R_b) = R_{gcd(a,b)}$;
  $R_{ab}/(R_aR_b)$ is an integer only if $gcd(a,b) = 1$, where $a\geq1$,
$b\geq1$ are integers. Dividers of numbers repunit, are researched by a degree
of prime number.
