|Figurate Pentagonal numbers are made by
successively stacking dots on a single dot to make nested pentagonal
figures. A count of dots at each addition gives the series 1, 5, 12,
22, 35, and so on.
the pentagonal numbers have unexpected properties. Take the 118th
Pentagonal number, 20827. Add it to its own reversal, and you have
93629, a prime number.
Find all 5-digit Figurate Pentagonal numbers which, when added to their own reversal, make a prime number.