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Re: [PrimeNumbers] A prime puzzle for you

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  • mikeoakes2@aol.com
    In a message dated 30/09/02 17:05:38 GMT Daylight Time, ... Correct (of course!), so congrats to David for spotting what was going on. The background is that I
    Message 1 of 5 , Sep 30, 2002
      In a message dated 30/09/02 17:05:38 GMT Daylight Time,
      d.broadhurst@... writes:


      > The solution is 4722079
      >
      Correct (of course!), so congrats to David for spotting what was going on.

      The background is that I got into investigating this property of the primes
      by wondering whether, for those various formulae of the type f(p) = a^p + ...
      for which one can show that any prime factor must be of the form q=2*k*p+1,
      one might stand a better chance of finding a prime by concentrating searches
      on exponents for which the minimum k in this expression was particularly
      large, thereby maximising the number of potential factors which did NOT
      divide the number. (The above solution has k_min = 117, no less!)

      So I chose 1163 (another "good" one) as exponent and very quickly found the
      PRP
      401200895^1163-401200894^1163
      which I submitted to Henri's database a couple of days ago.

      However, by examining the k_min values of the Mersenne exponents, and a
      couple of other examples, it appears that this optimism is unfortunately
      unfounded.

      Unless others can counter this conclusion?

      Mike



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