Friday, April 20

Eight

845534401, 83565065201, 829144019201, 834854554601, 854516148301, 866422665701, 878554044001, 889419071111, 890750408711, 891079866601, ...

Each of these is a prime equal to a multiple of its reversal plus-or-minus a prime smaller than itself in exactly 8 ways (A182239). For example:

845534401 = 104435548 *  3 + 532227757
          = 104435548 *  5 + 323356661
          = 104435548 *  6 + 218921113
          = 104435548 *  8 +  10050017
          = 104435548 *  9 -  94385531
          = 104435548 * 11 - 303256627
          = 104435548 * 14 - 616563271
          = 104435548 * 15 - 720998819

All ten of our numbers begin with an 8. What will be the first term that does not?

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