- 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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http://auctions.yahoo.com/ - On Sat, 05 May 2001, Anonymous Anonymous wrote:
> I have been fooling around with some trigonometric

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

> 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?

Phil

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http://www.shopping.altavista.com - 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