| Prime Time | What's really going to bake your
noodle is that later you'll think:"Would I still have broken
the vase if she didn't say that?"
--- Oracle--- . MARTIX |
|
This pattern has emerged during work on prime
numbers. Ray TOMES
has come across similar pattern years ago while working on HARMONICS THEORY.
No matter which way you go you will be always dealing with the same law
that governs this world. Principal used here is similar ( if not taken
from ) Sieve of Eratosthenes. The difference is the way the numbers are
positioned and dealt with and parallelism of the approach. Let's go.
Fig. 1 Excluding all the even ( if N(mod 2)=0 then discard N ) numbers leaves all possible primes mixed with their multiples. The pattern takes a shape of "rays" ( Hi, Ray :) )where each number down the ray is N*p ( p - position from the beginning ). Same is true for m, where m is any "row" across the ray pattern. Fig. 2 If a number of the first ray occurs only once in the "column" - it is a prime number. Fig. 3 For each number (M) in the first ray we produce a stream (a row) of numbers that are the multiples of that number (Z). For each multiple we can start a row from that number Z. Row Z will allow us to find non prime numbers faster than a propagation of the row M. Thus for any given suspect prime (X) the final row may consist of one number that is X/2 -1 or X/2 +1. The propagation takes place most of the time in the row with smallest M and towads its end, since the density of steps is higher. Now it is possible to "skip" some numbers in the smallest M row considering the results from the rows that are multiple of M because those rows make "larger" steps, thus achieving effect of sieve. Fig. 4 As in Fig 4 in row "3" we do not have to wait for propagation to reach "27" since the "child" row with a seed of "9" gets us in one step to "27" ( we discard all EVEN numbers , remember ? ) and we know that "27" is a multiple of the prime "3". Optimizing the process flow further by freeing up the resources that were used to exhaust already known search space it is possible to achieve faster speed. One of the tasks is to keep track on "collision" count , or the number of the occurences in a column since we can not assume that the number is prime unless all preceeding threads have gone past the value of that number and none of them produced such number. |
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