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18884[PrimeNumbers] Re: R109297

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  • Andy Steward
    Apr 25, 2007
      From: julienbenney
      Sent: 22 April 2007 14:32

      >Maybe they should search other bases. I recall reading tables of
      >generalised repunit primes for bases up to 51 (for base 51, there were
      >none at all up to the limit of n=2609).

      Phi(4229,51) is PrP. The first base for which I have not yet found a PrP
      is 152. There are 34 others under 1000 (excepting perfect powers)
      without a PrP, all have been searched for (prime) exponents up to 2^15.

      I can find no hints as to covering sets that would exclude any of these.

      >For instance, what is the next number in the sequence 3, 43, 73, 487,
      >2579, 8741, ...??

      37441 is a candidate. The answer lies in (10177,37441].
      (Base-15 PrP GRUs.)

      I should do a OEIS search and update whichever sequences I can. Last
      time I checked, I had "first base for each exponent" and "first exponent
      for each base" considerably improved from the published sequences, but
      that was years ago and someone else may have been working on them.

      There's too much "real life" going on atm ;-)

      Best Regards,
      Andy Steward
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