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…
If you found your A on table A1 multiply your C by 6 and add 1,
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)
