I am not a mathematician. But I think I may have stumbled into something interesting.
I wanted to try to make a number Prime Number table where multiples of 5 would line up. I wanted to line up the sequence of numbers of 5 6 7. The next one occurs at 35 36 37. So I thought by adding 30 to each row I could create a column of Composite Numbers of the multiples of 5. Not only did the first column contain multiples of 5, but all the numbers in the table lined up in sets of columns:
(-1 / x6 /+1 )( x2/ x3 / x2 )( -1 / x6 / +1 )( x2 / x3 / x2 )( -1 / x6 / +1 )( x2 / x3 / x2 )( -1 / x6 / +1) and so on
Or more simply expressed, using only the possible prime numbers (6n+ or- 1):
05 07 11 13 17 19 23 25 29 31
35 37 41 43 47 49 53 55 59 61
65 67 71 73 77 79 83 85 89 91
So by adding 30 to each row, all the multiples of 5 (using 6n+ or-1) lined up in two columns. In the first column the multiples were: 35 65 95 125 155 185... and in a second column, which included the square of 5, the multiples were: 25 55 85 115 145 175. Oddly enough 30 which I had added to the PN and each following row was 6 times the PN.
So I wondered if PN+(PNx6) would work for the prime number 7. This calculation using 7 identified: 49 91 133 175 217 259...
For 11, the calculations were: 77 143 209 275 341 407 473.. And there was again a second column with the square of 11 with the calculations of: 121 187 253 319 385 451 ... This process seemed to be identifying every composite number in the list of Possible Prime Numbers, one calculation for each composite number.
. . .5 . . .7 . .11 . . 13 . .17 . . 19 . . 23 . (25) . .29 . .31
(35) . .37 . .41 . .43 . .47 . (49) . 53 . (55) . .59 . .61
(65) . 67 . . 71 . .73 . (77) . 79 . . 83 . (85) . 89 . (91)
(95) . 97 . 101 . 103 . 107 .109 . 113 (115) .119 .(121)
(125) 127 .131 (133) .137 .139 (143)(145) .149 . 151
and the Table for the PN 17 identifies 119 as a composite number: 17+(17x6=102)
The tables were also very interesting. As with the PN 5 Table, all the numbers lined up in groups of columns. There were only two slight variations: The 6n-1 Tables had one pattern and the 6n+1 Tables had another which makes sense.
I have tried to figure out why this worked so well. The calculations from the Tables created a systematic method of cross multiplying the (A) 6n-1 numbers with the (B) 6n+1 numbers.
The 6n-1 Tables calculated AxB and AxA;
The 6n+1 Tables calculated BxB and BxA
However, the second column of BxA were duplicate calculations and could be discarded.
Some of multiples of 5 are duplicated but act more like a spacer than a duplicate and are part of the Table that are created by each Prime Number. I am going to upload a number of pictures that show the process and results. I appreciate you patience. I feel somewhat illiterate trying to express myself in a mathematical fashion.
I can't add the pictures at this time but here are a couple of links.