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Trigonometric functions with prime numbers?

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  • Anonymous Anonymous
    I have been fooling around with some trigonometric functions and I have noticed an easy primality test with them. One simply plugs in a number p into the
    Message 1 of 3 , May 5, 2001
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      I have been fooling around with some trigonometric
      functions and I have noticed an easy primality test
      with them. One simply plugs in a number p into the
      equation, and if the answer is an integer, than the
      number p is prime! Have there been any recent or
      non-recent discoveries relating trigonometic functions
      to prime numbers?

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    • Phil Carmody
      ... If you permit cosh to be considered trigonometric (it can be reformulated in terms of sin and cos with splashings of sqrt(-1)), then according to
      Message 2 of 3 , May 5, 2001
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        On Sat, 05 May 2001, Anonymous Anonymous wrote:
        > I have been fooling around with some trigonometric
        > functions and I have noticed an easy primality test
        > with them. One simply plugs in a number p into the
        > equation, and if the answer is an integer, than the
        > number p is prime! Have there been any recent or
        > non-recent discoveries relating trigonometic functions
        > to prime numbers?

        If you permit 'cosh' to be considered trigonometric (it can be reformulated in terms of sin and cos with splashings of sqrt(-1)), then according to http://www.utm.edu/research/primes/prove/prove3_2.html

        <<<
        Joerg Arndt notes that a striking (but computationally useless) way to state this test is as follows:

        Theorem: p=2^n-1 is prime if and only if p divides cosh(2^(n-2)log(2+sqrt(3))).
        >>>

        So, what's your formula then?

        Phil

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      • d.broadhurst@open.ac.uk
        ... Here s an extremely useless, yet mathematically correct trig test: C(n)=(cos(pi*((n-1)!+1)/n))^2 For n 1, C(n)=1 if and only if n is prime :-) Ribenboim
        Message 3 of 3 , May 5, 2001
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          progboy1 wrote:

          > I have been fooling around with some trigonometric functions

          Here's an extremely useless, yet mathematically correct
          trig test:

          C(n)=(cos(pi*((n-1)!+1)/n))^2

          For n>1, C(n)=1 if and only if n is prime :-)

          Ribenboim credits this piece of nonsense to someone
          called Willans.

          David
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