1993 OIM Problems/Problem 1

Problem

A natural number is a palindrome if, when written in decimal notation, it is the same when written from left to right and from right to left; for example: 8, 23432, 6446.

Let $x_1<x_2 < \cdots < x_i<x_{i+1}< \cdots$ be all the palindromes. For each $i$ , let $y_{i+1} = x_{i+1}-x_i$ .

How many different prime numbers does the set $\{y_1,y_2,y_3,\cdots \}$ contain?

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com ~ Edits by eevee9406

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1993 OIM Problems/Problem 1

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