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22578Re: [PrimeNumbers] Relatively major problem ripe for expansion

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  • Jens Kruse Andersen
    Feb 7, 2011
      James Merickel wrote:
      > On another note, I haven't heard back from Jens on an offer of sharing
      > credit for a nice titanic curio I put in his hands for proof, leading me to
      > believe he's working on it. I don't suppose there's likely to be any harm
      > done by stating it now, since he would have had quite a number of hours with
      > it. The first titanic near-repunit prime with a near-repunit prime number
      > of digits, (10^1117-1)/9+4*10^92, is the 101st such prime (of any size),
      > assuming no rare ispseudoprime false positive and defining near-repunits to
      > necessarily have at least 3 digits.

      You mailed me less than a day ago. Following up on your work is not all I do,
      and I don't want to share a curio just because I verified it afterwards.
      However, after seeing your post here I have confirmed it is the 101st prp.
      Marcel Martin's Primo has proved the first 77 prp's and the last.
      I skipped the remaining 23 which have 811 and 911 digits:
      (10^811-1)/9+6*10^14
      (10^811-1)/9+6*10^82
      (10^811-1)/9+4*10^115
      (10^811-1)/9+6*10^155
      (10^811-1)/9+7*10^216
      (10^811-1)/9+7*10^242
      (10^811-1)/9+7*10^388
      (10^811-1)/9+7*10^406
      (10^811-1)/9+4*10^480
      (10^811-1)/9+6*10^530
      (10^811-1)/9+4*10^577
      (10^811-1)/9+1*10^600
      (10^911-1)/9+8*10^327
      (10^911-1)/9+6*10^357
      (10^911-1)/9+6*10^402
      (10^911-1)/9+5*10^465
      (10^911-1)/9+2*10^475
      (10^911-1)/9+6*10^707
      (10^911-1)/9+5*10^717
      (10^911-1)/9+8*10^732
      (10^911-1)/9+6*10^792
      (10^911-1)/9+6*10^795
      (10^911-1)/9+2*10^890

      It might take around half a GHz day to verify them with Primo from
      http://www.ellipsa.eu/public/primo/primo.html

      The 23 input files can quickly be made with
      http://users.cybercity.dk/~dsl522332/math/certif/primoin.zip

      --
      Jens Kruse Andersen
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