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

Integral equation with prime solutions

Expand Messages
  • Sebastian Martin Ruiz
    Theorem:   Let x a real number x 2   x is a prime number if and only if:   Integrate[Ceiling[x/Floor[y]-Floor[x/Floor[y]]], {y,2,Floor[x]-1}]=x-3      
    Message 1 of 1 , Aug 22, 2012
      Theorem:
       
      Let x a real number x>2
       
      x is a prime number if and only if:
       
      Integrate[Ceiling[x/Floor[y]-Floor[x/Floor[y]]], {y,2,Floor[x]-1}]=x-3
       
       
       
      For this you can check
       
      G[x_]:=Sum[NIntegrate[Ceiling[x/Floor[y]-Floor[x/Floor[y]]],{y,i,i+1},MaxRecursion->6],{i,2,x-2}]
       
       
      Do[Print[G[x]," ",x," ",PrimeQ[x]," ",x-G[x]],{x,3,200,1}]
       
       
       
      Sincerely:
       
      Sebastian Martin Ruiz

      [Non-text portions of this message have been removed]
    Your message has been successfully submitted and would be delivered to recipients shortly.