Neglecting the trivial solutions(0 and 1),
the first 50 digits of
our numbers in several digit-systems (base 2 to 36) are
listed in the following table.
When writing a number in base p in the table,
the digits used can range from 0 to p-1.
If p>10, then the digit ``a'' stands for 10,
``b'' for 11, etc.
There is no non-trivial solution in some base.
Although it is conjectured that the number of non-trivial solution
would be 2 when they exist, the conjecture breaks down at p=30.
Here has arisen another conjecture in which
there is no non-trivial solution in particular base p such that
the sort of the divisor of p is only one. Though this conjecture
seems to be correct according to the case ( 
) listed,
it does not have the proof yet.