By now, you should all be aware of my belief that the entire prime family is dependent on, and revolves around the number 24.
Firstly, take a look at the following table and don't be to concerned about the content at this point, as all will be explained shortly.
For the moment, focus on the column titled "Square root / Prime" and spend a few moments examining it.
This table basically shows how simple it is to generate EVERY odd number sequentially by a simple arithmetical process, which I'll explain
As should be immediately obvious, this column simply lists all the odd numbers from 1 to 101 sequentially. The two important points to be aware of
when looking at this column is (a) the numbers were generated in this sequence by simple arithmetic; and (b) the prime numbers have been highlighted
Now, here's how simple arithmetic is used to generate the sequential odd numbers in the final column (Square Root / Prime)
The columns titled "Increment" and "Running total" go hand in hand.
Basically, the "Increment" column starts at 0 and has 8 added to it in each row. So it starts at 0, has 8 added to it to give a total of 8, then has
another 8 added to it to give a total of 16, then another 8 added to give a total of 24, and so on all the way down the "Increment" column.
The "Running total" column starts with 1 and has the corresponding "Increment" value for that row added to it. So it starts with 1 and has 0 added
to it from the "Increment" column (for that row) giving a running total so far of just 1.
Then we move to the next row and take the "Increment" value of 8 and add it to the previous "Running total" value of 1 to give a new "Running
total" value of 9.
Now we move down another row and add the "Increment" value of 16 to the previous "Running total" value of 9, and getting a new "Running total"
value of 25.
And so on all the way down the table.
Confused ??? I'll bet you are !
So, how about a picture to make it easier to follow ...
Notice that in the "Square root / Prime" column that both 1
have been highlighted in red
to indicate that they are PRIME.
Now take a look at the "Multiple of base 24" column entry.
The 8+16=24 entry is there simply to show that a total of 24 (or multiple) has been accumulated by adding the current "Increment" value to previous
The (1x24) entry is there to simply show whether we have a single value of 24 or a multiple value of 24.
Now the interesting part of all this rambling of mine is to highlight a very curious and interesting feature of this table. Even though this table
basically justs generates a (theoretical) infinity of sequential odd numbers, notice that EVERY prime number (Square root / Prime column) has an
associated "Multiple of base 24" entry ... again indicating the powerful role played by the value 24 within the entire prime family !
To illustrate this effect, in the following table, I've removed all non-prime rows.
I don't know if you're amazed and surprised by this unexpected revelation ... I know I certainly am !