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Prime number proof

  1. Sep 28, 2013 #1
    prove if the statement is true, else form it's negation and prove that is true:

    ## \forall y \in (x | x \in \mathbb Z , x \geq 1), 5y^2 + 5y + 1 ##

    I think it's true, but I can't really even get started to prove it

    I really suck at these and need help please, thank you!
     
  2. jcsd
  3. Sep 28, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    There is no statement that could be evaluated as true or false.
    It is like "prove that this is true or false: 5".

    I guess there is "is prime" missing. Did you test some numbers to check it? Don't just check small numbers, consider larger numbers as well.


    Big hint:
    There is no known useful formula to generate an arbitrary number of primes without excessive calculations.
     
  4. Sep 28, 2013 #3
    Put this text into an *.vbs file and run it:

    For y = 1 To 100
    z = 5*y*y + 5*y + 1
    if (z mod 11)=0 then MsgBox("f(" & y & ") is divisible by 11.")
    if (z mod 19)=0 then MsgBox("f(" & y & ") is divisible by 19.")
    Next
     
  5. Sep 29, 2013 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Where did "divisible by 5" and "divisible by 11" come from?
     
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