[ *January 4, 2000* ]

Palindromic_free squares, cubes and primes

In this paragraph I am searching for the largest **Square** and **Cube** whose decimal expansion

contains __no palindromic substrings__ except of course their single digits themselves.

Square Root | Palfree Square |

**10104574 ***( first above 10*^{7} ) | **102102415721476 ***( length 15*^{ }) |

Cube Root | Palfree Cube |

**10069605 ***( first above 10*^{7} ) | **1021027182906953620125 ***( length 22*^{ }) |

Info | Palfree Prime |

*( first above 10*^{7} ) | **10210219 ***( length 8*^{ }) |

All these examples our put in the table only as a starting point.

Your task is to find the largest possible palfree square, cube and/or prime.

My guess is that the above record palfree numbers will be approximately 45 digits long ...

but I could be wrong!

Good luck with this research topic and keep me posted!

This plate is a prequel to WONplate 46