Fuck it ill just show how to do it.
Make a software based slide rule, except unlike a normal slide rule you need 8 slides to really see what's going on 7 of the slides move independently and the 8th is just a number line that stays locked to make it easy to know where you are.
Start at the center with
-3, -2, -1, 0, 1, 2, 3 ; 0
On lines 1 thru 7 you subtract 6 above and add 6 below. On the 8th line its subtract 1 above and add 1 below. So it looks like.
-9, -8, -7, -6, -5, -4, -3; -1
-3, -2, -1, 0, 1, 2, 3; 0
3, 4, 5, 6, 7, 8, 9; 1
Visualize this as vertical rows that are locked together but the first 7 can slide up or down. With the 8th remaining stationary.
Now choose the (RMA) composite you want to factorize. I'll do the first one which is 5×5 = 25. And lay it out for a visual as to why this leads to the prime you want. First using the two rows beside the center where 25 is located slide the 25 and -25 up and down respectively until they are beside 0.
Now multiply the composite by 2, which in this case gives you 50. Slide the +50 and -50 down and up respectively until they are next to -25 and +25.
Then multiply by 3, in this case getting 75, and repeat the above. You will end up with.
-75, -50, -25, 0, 25, 50, 75; 0
Now lock the first 7 rows together with the 8th row. they no longer move. If you do this then look the only primes that will be lined up with numbers they divide into will be the 5's.
Note this can be done also using only 2 lines, but it doesn't help u visualize how it works.
-55, -5; -5
-49, 1; -4
-43, 7; -3
-37, 13; -2
-31, 19; -1
-25, 25; 0
-19, 31; 1
-13, 37; 2
-7, 43; 3
-1, 49; 4
5, 55; 5
Doing the whole diagram is to much typing, hope you like the smaller version.
