Testing if a number N is prime by its regular polygon's angles

Question

Is it possible to tell if a number N is prime by looking at the angles of a regular N-sided polygon? For example, a regular triangle has 60 degree angles, is there a way to tell that the number 3 is prime from its polygon's sides being 60 degrees?

(Not a math person so forgive my poor explanation)

Answer 1

Suppose you test larger prime/noprime number p(n). If you know two nearest real primes p(n-1) and p(n-2) and if you consider that p(n), p(n-1), p(n-2) are sides of a triangle, then p(n) is prime when the angle between p(n-1) and p(n-2) is nearby 60 degrees.