Loading ...
Sorry, an error occurred while loading the content.

Two elementary conjectures

Expand Messages
  • Patrick Capelle
    Dear List, A few days ago i proposed two conjectures. Conjecture A : Every natural number n 1 can be written as n = pq + rs, where p, q, r, s are primes or
    Message 1 of 2 , Oct 8, 2006
    • 0 Attachment
      Dear List,
      A few days ago i proposed two conjectures.

      Conjecture A :
      Every natural number n > 1 can be written as n = pq + rs,
      where p, q, r, s are primes or 1.

      Conjecture B :
      Every natural number n > 33 is the sum of two semiprimes.

      Carlos Rivera checked them up to 10^6.

      The conjecture A and the conjecture B were inspired respectively by
      the Papadimitriou's conjecture and the Firoozbakht's conjecture .

      Papadimitriou's conjecture :
      Every prime number p > 3 can be written as p = 2q + 3r,
      where q, r are primes or 1.

      Firoozbakht's conjecture :
      Every prime number p >= 19 can be written as p = 2q + 3r,
      where q, r are odd primes.

      About the conjecture B, Farideh Firoozbakht mentioned recently that
      Lior Manor had already written on this topic (Aug 13 2002):
      http://www.research.att.com/~njas/sequences/A072966

      Do you know other former references ?

      Patrick Capelle
    • Patrick Capelle
      ... I added some comments to the following address : http://www.primepuzzles.net/conjectures/conj_049.htm Best regards, Patrick Capelle
      Message 2 of 2 , Oct 15, 2006
      • 0 Attachment
        --- In primenumbers@yahoogroups.com, Patrick Capelle wrote :

        > Dear List,
        > A few days ago i proposed two conjectures.
        >
        > Conjecture A :
        > Every natural number n > 1 can be written as n = pq + rs,
        > where p, q, r, s are primes or 1.
        >
        > Conjecture B :
        > Every natural number n > 33 is the sum of two semiprimes.
        >
        > Carlos Rivera checked them up to 10^6.
        >
        > The conjecture A and the conjecture B were inspired respectively by
        > the Papadimitriou's conjecture and the Firoozbakht's conjecture .
        >
        > Papadimitriou's conjecture :
        > Every prime number p > 3 can be written as p = 2q + 3r,
        > where q, r are primes or 1.
        >
        > Firoozbakht's conjecture :
        > Every prime number p >= 19 can be written as p = 2q + 3r,
        > where q, r are odd primes.
        >
        > About the conjecture B, Farideh Firoozbakht mentioned recently that
        > Lior Manor had already written on this topic (Aug 13 2002) :
        > http://www.research.att.com/~njas/sequences/A072966
        >
        > Do you know other former references ?
        >
        > Patrick Capelle

        -----------------------------------------------------------------

        I added some comments to the following address :
        http://www.primepuzzles.net/conjectures/conj_049.htm

        Best regards,
        Patrick Capelle
      Your message has been successfully submitted and would be delivered to recipients shortly.