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Math Help - Testing Riemanns Hypothesis - need help

  1. #1
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    Testing Riemanns Hypothesis - need help

    I've read a few articles about how several researchers have tested large ranges of prime numbers and I am interested on how they are doing this.
    1) Does anyone have the software equation used to test prime numbers? In C++,xBase or Visual basic would be useful.
    2) How is the result used to determine that it is in the correct range? I'm looking for a simple description if possible.
    3) What happens if non-prime numbers are plugged into this equation and they give results that mirror the results of prime numbers? Would that invalidate the equation?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    The Riemann Hypothesis is true  \Longleftrightarrow | \pi(x) - li(x) | < \frac{1}{8\pi}\sqrt{x}\log(x) \;\;\;\;\; \forall \; x>2657 .

    Is this what you're referring to when you say "test prime numbers"?
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  3. #3
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    Testing prime numbers

    Hi
    I'm looking for a software routine that I can use to test primes. My simple understanding of Riemann's Hypothesis is that prime numbers occupy special positions and I'm aware that so far, all testing of prime numbers against the Hypothesis have confirmed that they all occupy these positions.

    My other questions were to do with how to interpret the result of plugging in a prime number into this routine - i.e. what would one expect to see for a prime number but also what would one expect to see for a non-prime number.

    Thanks!
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Could you give me an example of this routine you're talking about using a prime number that's three digits long?
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  5. #5
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    Software routine

    I don't have a routine myself - I'm looking for one that someone else has. I understand some of the equation you've given but not enough to translate it into a software routine.
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  6. #6
    MHF Contributor chiph588@'s Avatar
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    I'm still trying to understand what your routine is. You're pretty ambiguous about it.
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  7. #7
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    Software routine

    I've read several articles describing how mathematicians have used their university's super computer to test large prime numbers when there is spare capacity available. The results were apparently consistent with Riemann's Hypothesis.

    That means that they had a software routine that they were able to use for that testing.

    1) I'd like to know what that routine is, in readable computer program code
    2) How to interpret the result from using a prime number as an input
    3) What the implications are of using a non-prime number which could conceivably generate a result consistent with prime numbers.

    I don't know enough about that testing process to maybe ask the right questions, but having programming experience I know that someone should have a routine they could make available.

    In other words if z() represents the function then z(prime) gives a result which has meaning for this hypothesis.

    For example 107 as a prime number - how is this tested to see if it conforms to the Hypothesis?
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