WON plate143 | World!OfNumbers [ November 12, 2002 ] Palindromic Primes stretching out until... by Jeff Heleen (email) I have found 3 palprimes. I don't know if you have them somewhere already on your site but here they are. If you start with a central 1 and concatenate the counting integers to either side (mirrorwise to the left),the palprimes occur at N = 31, 59 and 113, all three N values are coincidentally prime ! 1303928272...7654321234567...2728293031 = prime (105 digits) 9585756555...7654321234567...5556575859 = prime (217 digits) 311211111011...4321234...110111112113 = prime (417 461 digits) My search went up to N = 999. I used Primo for the tests. Who can extend this list with a few more terms ? [November 15, 2002 ] Jean Claude Rosa wrote that the third number had a wrong length indication 417 instead of 461. "Soit P = n... ...32123... ...n avec 99 < n < 1000 pour avoir la longueur de P j'utilise la formule suivante : longueur de P = 6 * n - 217 Si n = 113, longueur de P = 6 * 113 - 217 = 461." [November 17, 2002 ] Jeff Heleen has another possible palprime for this plate. For N = 1277 (a prime itself) shows promise. This would yield a number with 8001 digits (assuming I have added correctly). I shall not attempt to prove it prime at this time as it would take far too much time. PDG tested this candidate with PFGW [July 13, 2004 ] but to my surprise the outcome was that this number is composite ! In case I made a mistake perhaps someone would like to confirm that this palindrome is not a probable prime ? A000143 Prime Curios! Prime Puzzle Wikipedia 143 Le nombre 143
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