Trigonometric functions with prime numbers?
- 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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- On Sat, 05 May 2001, Anonymous Anonymous wrote:
> I have been fooling around with some trigonometricIf 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
> 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?
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?
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- progboy1 wrote:
> I have been fooling around with some trigonometric functionsHere's an extremely useless, yet mathematically correct
For n>1, C(n)=1 if and only if n is prime :-)
Ribenboim credits this piece of nonsense to someone