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Conjecture for integer linear combinations of primes

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  • Sebastian Martin
    Hello All: I send a new conjecture: Conjecture for integer linear combinations of primes ...   Let n a even number , for all 2
    Message 1 of 2 , May 5, 2008
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      Hello All:
      I send a new conjecture:
      Conjecture for integer linear combinations of primes
      :
       
      Let n a even number , for all 2<=k <=n/2 exists one or more integer linear combination:
       
      a1p1+a2p2+…..+ampm=n  
       
      and
       
      a1+a2+…+am=k
       
       
      p1,p2,…., pm are all the prime numbers less than n
      and ai>=0 integer
       
      Example:
       
      n=10   n/2=5
       
       
      p1=2, p2=3  p3=5 p4=7
       
       
      2*5=10                     a1=0, a2=0, a3=2, a4=0      Sai=2
      1*3+1*7=10             a1=0, a2=1, a3=0, a4=1      Sai=2
      1*2+1*3+1*5=10     a1=1, a2=1, a3=1, a4=0      Sai=3
      2*2+2*3=10             a1=2, a2=2, a3=0, a4=0      Sai=4
      5*2=10                     a1=5, a2=0, a3=0, a4=0      Sai=5
       
       
      Q1=Is true or false this Conjecture.
      Q2=¿ We can obtain Goldbach Conjecture as a particular case of this conjecture?
      Sincerely:
      Sebastián Martín Ruiz


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    • Kermit Rose
      1. Conjecture for integer linear combinations of primes Posted by: Sebastian Martin sebi_sebi@yahoo.com sebi_sebi Date: Mon May 5, 2008 4:10 am ((PDT)) Q1=Is
      Message 2 of 2 , May 6, 2008
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        1. Conjecture for integer linear combinations of primes
        Posted by: "Sebastian Martin" sebi_sebi@... sebi_sebi
        Date: Mon May 5, 2008 4:10 am ((PDT))




        Q1=Is true or false this Conjecture.
        Q2=¿ We can obtain Goldbach Conjecture as a particular case of this conjecture?
        Sincerely:
        Sebastián Martín Ruiz



        If Goldbach conjecture is true then your conjecture is true
        because the

        p1 + p2 = n = 2k is the one of one or more linear combination of primes that equal n.


        Your conjecture does not imply the Goldbach conjecture, because we can imagine that
        the set of linear combinations of primes that equals n, does not include a linear combination of the
        form p1 + p2 = n.


        Kermit Rose


        < kermit@... >
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