Idle thoughts
Jul. 10th, 2003 10:00 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
lionkingcmslWhile driving home tonight, from the railroad, I had some interesting thoughts about prime numbers. You know, those numbers that can only be divided by themselves and one.
It came to my attention, and I'm sure that someone has noticed it before, that out of the single digit prime numbers (1, 2, 3, 5, 7) only two of them are only prime by themselves. If they end a multi-digit number then that number can no way be prime.
For example 11 is prime, but 21 is not, so 1 can not be one of those numbers.
And these two numbers have an interesting relationship.
The two numbers are 2 and 5.
Now here is the interesting part. Any number that is multiplied by 2 to get an nnn2 has to end in a 1 or a 6; i.e. 6*2=12, 11*2=22, 16*2=32, and so on.
Now with 5, all the numbers have to be odd to multiply by 5 to get a nnn5 number.
You can only get an nnn5 by multiplying an odd number by 5, or a multi-digit nuber that ends in 5. No other combination works.
Now here is the relationship between 2 and 5 in this situation. The difference between 1 and 6 is 5. The difference between the odd numbers is 2. Also there is only one prime number between 2 and 5 and that happens to be 3. We all know, of course, that 2+3=5.
Again, some interesting things that had popped into my head as I was driving.
BTW, I didn't include 0 (zero) in the above, as most math people don't really consider it a true number. It is a "null set".
It came to my attention, and I'm sure that someone has noticed it before, that out of the single digit prime numbers (1, 2, 3, 5, 7) only two of them are only prime by themselves. If they end a multi-digit number then that number can no way be prime.
For example 11 is prime, but 21 is not, so 1 can not be one of those numbers.
And these two numbers have an interesting relationship.
The two numbers are 2 and 5.
Now here is the interesting part. Any number that is multiplied by 2 to get an nnn2 has to end in a 1 or a 6; i.e. 6*2=12, 11*2=22, 16*2=32, and so on.
Now with 5, all the numbers have to be odd to multiply by 5 to get a nnn5 number.
You can only get an nnn5 by multiplying an odd number by 5, or a multi-digit nuber that ends in 5. No other combination works.
Now here is the relationship between 2 and 5 in this situation. The difference between 1 and 6 is 5. The difference between the odd numbers is 2. Also there is only one prime number between 2 and 5 and that happens to be 3. We all know, of course, that 2+3=5.
Again, some interesting things that had popped into my head as I was driving.
BTW, I didn't include 0 (zero) in the above, as most math people don't really consider it a true number. It is a "null set".
