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18877R109297

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  • julienbenney
    Apr 21, 2007
      It's odd I just came to think of primes as I came in after the first rain in Melbourne for weeks.
      I was reminded of the proof of the primality of R317 and just looked up "repunit prime" on
      Wikipedia, expecting to find nothing at all that I did not already know.

      When I checked it, however, I found, to my greatest surprise, that Harvey Dubner had found
      yet another probable repunit prime with 109297 copies of the number one. It was Dubner
      who found, after a lengthy search when for a long time he did not expect to find a repunit
      prime, the previous probable prime repunits R49081 and R86453.

      The distance between R1031 and R49081 and the fact that there seemed to be three "pairs"
      of repunit primes or PRPs (19 and 23, 317 and 1031, 49081 and 86453) made me think
      intuitively that the next PRP repunit would be extremely large. I imagined when I first saw
      R86453 to be a probable prime that the next PRP repunit would have over one million digits -
      sometimes imagining it to be one of the numbers of the prime quadruples beginning with
      1,006,301 and 1,006,331. Having seen R109297, I can imagine the next PRP repunit having
      several million digits - Dubner himself intends only going to 200,000 and I do not know what
      to say if there is another PRP repunit up to that small a number of digits.
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