# Thread: My Prime Number Matrices. Useful/Just another sieve?

1. ## My Prime Number Matrices. Useful/Just another sieve?

The factors of any prime-like number (for this definition a number not divisible by 2 or 3) can be found by dividing it by 6 +-1 and placing it on its' specific matrix.

Are these tables useful in creating a pattern out of primes or is this just another sieve that I've made?
I'm a non-maths guy but I've really had fun playing with primes for the last few weeks so I don't mind if all I do is keep creating sieves, you never know I might get there eventually...

Table A1 (Both factors are of the form 1+6,+6...)

________________C1______C2______C3______C4______C5_____C6
D1______________8_______15______22______29______36 ______43
D2______________15______28______41______54______67 ______80
D3______________22______41______60______79______98 ______117
D4______________29______54______79______104____129 _____154
D5______________36______67______98______129____160 _____191
D6______________43______80______117_____154____191

Table A2 (Both factors are of the form -1+6,+6.…)

________________C1______C2______C3______C4______C5_______6
D1______________4_______9______14_______19______24 ______29
D2______________9_______20_____31_______42______53 ______64
D3______________14______31_____48_______65______82 ______99
D4______________19______42_____65_______88_____111 _____134
D5______________24______53_____82_______111____140 _____169
D6______________29______64_____99_______134____169 _____204

Table B (One factor on -1+6,+6... & One factor on 1+6,+6...)

_________________C1_____C2______C3_____C4______ C5
D1_______________6______13______20_____27_______34
D2_______________11_____24______37_____50_______63
D3_______________16_____35______54_____73_______92
D4_______________21_____46______71_____96______121
D5_______________26_____55______84_____113_____142
D6_______________31_____66______101____136_____171

Take any number that is not divisible by 2 or 3 call it X
(for this example a number < 1000 if you want to find it on the matrices above)

(X-1)/6=A (Only if A is a whole number otherwise discard it)
(X+1)/6=B (Only if B is a whole number otherwise discard it)

(Every number not divisible by 2 or 3 will either be an A or a B)

If you have an A find it on table A1 or A2.

When you have found A get a C value from the top…

This is one of the factors of X.

If you found your A on table A2 multiply your C by 6 and subtract 1
This is one of the factors of X.

If you did not find your A on A1 or A2 it is a prime number.

If you have a B find it on table B multiply your C by 6 and subtract 1 this is a factor of X.

If you did not find your B on table B it is a prime number.

(I derived the matrices from 6BC+B+C=A and 2 variations thereof)

2. Doh, nevermind, already been told it's pretty useless/std.

3. ## How modest

I'm a non-maths guy but I've really had fun playing with primes for the last few weeks
You can't say that forever, dude. This is pretty cool stuff you're contributing. Math is historically full of "amateurs" that left some pretty profound legacies (Fermat, Goldbach, Ramanujan, etc.). One thing you might do as a non-maths person is read up on some number theory to get a handle on basic theorems and open problems (ex: prove there's always a prime between $\displaystyle n^2$ and $\displaystyle (n+1)^2$ - currently unknown). As far as an all-encompassing "user-friendly" history of prime number research, I'd highly recommend Marcus du Sautoy's "Music of the Primes." You only think you're a non-maths guy, but you've caught the bug