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probability that a particular function of a prime would be prime

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  • Kermit Rose
    For each of the odd primes p
    Message 1 of 1 , Nov 19, 2006
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      For each of the odd primes p < 10 000, I calculated the number q as follows.

      r = int(5 * p/12)

      m = r - p%r

      q is the largest odd factor of m.

      There are 1228 odd primes < 10 000.

      Given that I select only the numbers q which are > 14, what would you
      guess would be the probability that q is prime?

      The maximum value of q in this set is 2489. q is not distributed
      uniformly. There are more q's in the range 1 to m, than in the range
      m to 2m, for every positive m sufficiently large.

      Would it surprise you to find that I counted
      590 composite values of q in this range,
      and counted
      591 prime values of q > 14 in this range?

      Kermit < kermit@... >
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