09 AUG 2014 by ideonexus

## 12X Spiral

The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 eggs in a carton, 12 inches in a foot, 12 months in a year, 24 hours in a day, 360 degrees in a circle, 60 seconds in minute? Because highly composite numbers can be divided evenly in many ways. For...Building a spiral around a clock, with 12-segments in the rotation, puts multiples of 3 at {3,6,9,12}, multiples of at {4,8,12}, multiples of 2 at {2,4,6,8,10,12}, and primes at {1,5,7,11}.

18 JUN 2013 by ideonexus

## Proof That the Set of Prime Numbers is Infinite

Theorem: There are infinitely many prime numbers. Proof: Suppose, contrary to the theorem, that there is only a finite number of primes. Thus, there will be a largest which we can call p. Now define a number n as 1 plus the product of all the primes: n = (2 X 3 X 5 X 7 X 11 X...X p) 1 Is n itself prime or composite? If it is prime then our original supposition is false, since n is larger than the supposed largest prime p. So now letâ€™s consider it composite. This means that it must be div...There is always one larger.