Figurate Pentagonals

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. |

Sometimes
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. |

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Last Updated: January 17th, 2010.