28 SEP 2021 by ideonexus

 Prime Numbers and Cryptography

Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then cross out all the numbers that are multiples of 2, besides itself (4, 6, 8, 10, 12, and so on). Take the next smallest number that hasn’t been crossed out (in this case, 3), an...
  1  notes
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...
  1  notes

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}.