a ratio between integers and primes (page 2)


the approximate ratio of,

#integers / #primes = arc length (of a circle) / y-length (of the spiral)

The x-length of the spiral, from O to A, equals the y-length of the circular arc, from O to A, relative to O. Therefore, as the circumference approaches a length infinitely large the approximate ratio between integers and primes can be defined as

#integers / #primes = x-length (of the spiral) / y-length (of the spiral) 2/π

x-length over y-length representing the value of (a) in the log spiral, then

#integers / #primes = (a)π/2

as the value of (a) grows to an amount approaching infinitely large.


Though the value of the ratio (a) can approach an amount infinitely large, this number is never more than a small fraction of the number of integers corresponding to the length of OA.