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18845Decomposition of primes : new algo

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  • reismann@free.fr
    Mar 31 5:44 AM
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      Dear primenumbers Group,

      With my friend fabien Sibenaler, we realized a Java program implementing the new
      algorithm that gives the decomposition of a prime number (prime = weight * level
      + gap, or A000040(n) = A117078(n) * A117563(n) + A001223(n)).
      This pgm is faster than the previous versions (Java and assembly said "naïfs").
      This pgm Java load a MySQL table.
      We look for the odd weights until sqrt (p) (zone 1) and if we did not find the
      decomposition, we look for it by levels until (ln p)^2 (zone 2).
      This limit is arbitrary and can be improved.
      A minimum is imposed to avoid exceptions and if the following conjecture is
      true, it should no more have exceptions :
      conjecture : Except for p(6), p(11), p(30), p(32) and p(154), the weight of
      prime numbers for which weight>level (zone 2) is prime.
      The pgm assembler will soon be modified.
      Java pgm :
      or on the "Download" page :

      Two new pages will soon be created on my site. One on the algorithmie and the
      other one on the conjectures based on my vision of prime numbers.


      Rémi Eismann