Unique Investigation of Primes
Started with a Simple New Formula:
S_k = S_k-1^P \_M P

• explains why this prime formula works (in essence, it expresses algebraically a method that superimposes structure upon the sieve of Eratosthenes)



• builds upon the following 5 key concepts, displayed in layers as:
  

  Symmetric Sequence Generator Symmetric Transform Transform Symmetric Sequence Sequence

• examines two types of symmetric sequences of integers, shows how they relate to each other and to primes, and then applies them in investigating primes



• introduces a second prime formula which is uniquely helpful:
  S_k = S_k-1^P \ (S_k-1 * P)



• establishes the conditions for which:
  S_k-1^P \_M P = S_k-1^P \ (S_k-1 * P)



• shows there are infinitely many structures useful in modeling prime numbers



• generalizes using a construct called a symmetric sequence generator, from which we see how the prime structures fit into a more general class of structures



• gives a new and unique proof of the infinitude of primes, and also a new and unique proof that prime gaps are not bounded



• explains and makes use of different avenues of investigating prime numbers



• discusses thorougly the following pattern and illustrates some of its practical uses:

  4 2 4 2 4
  8 4 2 4 2 4 8
  8 4 2 4 2 4 8
  16 8 4 2 4 2 4 8 16
  ... 4 ...

• provides novel derivations for numerous properties of primes



• highlights structures that provide insights into prime numbers even though they are essentially independent of primes

Prime Related Links

Here's a short list of interesting and instructive websites and webpages about prime numbers. Those less familiar with mathematics are advised to start with links in the left column.