20180102, 05:41  #166  
Dec 2017
110010_{2} Posts 
Quote:
Last fiddled with by George M on 20180102 at 05:42 

20180102, 06:47  #167  
Aug 2006
3^{2}×5×7×19 Posts 
Quote:
Last fiddled with by CRGreathouse on 20180102 at 06:47 

20180102, 07:36  #168  
Feb 2017
3×5×11 Posts 
Quote:
Thanks. I will read up more about this. My references/material are sourced mostly from Wikipedia and youtube. I will follow you link as well. Regards 

20180102, 16:54  #169  
Feb 2017
3·5·11 Posts 
Quote:
I read up on your link about wheel factorization, and it is unfortunately a bit too complicated for me to understand the math involved in wheel factorization fully at this stage. It seems as if one would need to have a postgrad qualification in wheel factorization to fully understand it. What I do is much simpler. I take the positive odd numbers and arrange them into grids of varying column numbers, and then look at the distribution patterns of the prime numbers. For example again, if I arrange the odd numbers into a 3column grid (or an array as one of the other contributors has suggested that it could be called), all the primes are then distrubuted in columns 1 & 3 respectively, and column 2 contains "3" and all the odd multiples of three. Column 3 contains all the chen primes, as well as all the squares of the odd numbers(including primes) in column 1. Column 1 contains all the primes that would follow after chen primes that is the second partner of twin primes, as well as the squares of the odd numbers (including primes) in column 3). Just some of the more obvious patterns eminating fro a 3column grid. As indicated in an earlier post, these tables have the property of being de facto primality sieves as well. The prime (and composites) in this grid3 distribution are distributed according to 6n+1, 6n1 consecutive order. Again the sieve factor can be algorithmized to identify the prime distribution in this grid. Grids with a prime number of columns, "filters" the multiples of that prime number located in the centre column of the grid. Grids with a composite number of columns "filters" all the prime factors of that composite odd number!! Another potential algorithm! which would read something as follows; For any XXXgrid of odd prime numbers with y number of columns, where y is an element of the set of odd numbers, then when y is prime, only one set of odd multiples of y would be distributed in the centre column of the the grid. If y is composite, the multiples of the prime factors of y will be "filtered" on both sides of the grid, with respect to the y(composite)multiples in the centre column. Caveat: Not sure if anybody else has done or publish similar work (Odd No.GridColumn no. relationships), but the above is only for information with respect to what I have worked with. 

20180102, 17:18  #170  
Banned
"Luigi"
Aug 2002
Team Italia
2·29·83 Posts 
Quote:
Patience, will and attention: if you lack such elementary attitudes, you will never, never succeed in math. Last fiddled with by ET_ on 20180102 at 17:19 

20180102, 17:20  #171  
"Composite as Heck"
Oct 2017
1433_{8} Posts 
Quote:


20180102, 18:31  #172  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9426_{10} Posts 
Quote:
Think about it. 

20180103, 00:26  #173 
Feb 2017
3×5×11 Posts 
Moving into Stormy Waters
My mom always used to teach me....Son, when you hear wolves howling in unison, protect the chickenpen!

20180103, 01:04  #174 
If I May
"Chris Halsall"
Sep 2002
Barbados
10010101100101_{2} Posts 

20180103, 01:21  #175  
"Dana Jacobsen"
Feb 2011
Bangkok, TH
2^{2}·227 Posts 
I'm sure there are plenty of other examples, some better, but a paper I ran across when I was first serously fiddling with these things, shows a number of similar charts (see page 106107 near the end). Arranging numbers in an array and noticing patterns of primes and composites is common.
"A Note on the Extensions of Eratosthenes' Sieve" by Quesada and Van Pelt, 1996. By today's standards this is pretty yawnworthy, but I personally gained some appreciation of the modular patterns from reading it, as well as some ideas for optimizing my SoE implementation back when I first started it (so many things I didn't know then....) I don't think the authors believed they were making really novel insights, but trying to make some helpful clarifications and noting patterns. Feel free to make these connections, not read anything of the previous work in the field, and believe you are a genius first discoverer. That's great. I am somewhat envious. But I'd also know I was lying to myself. Quote:
This is crankthought (there should be some cool German word for this). The more people disagree with you, the more you must be a misunderstood genius? 

20180103, 01:37  #176 
If I May
"Chris Halsall"
Sep 2002
Barbados
3·3,191 Posts 

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