This is the interesting fact: I can tell you whether a 3-digit number is a prime number (almost) instantly using mental arithmetic.
In hindsight, it's actually not really that interesting or unusual, if you consider the following:
(Warning: long technical, mathematical read ahead!)
Prime numbers are numbers which are divisible only by itself and the number 1. As an example, single-digit prime numbers are 2, 3, 5 and 7 while two-digit prime numbers are 29, 37 and 73.
Now, consider the total number of 3-digit number from 100-999. That is 900 numbers in total.
For any of the numbers in this range to qualify as a prime number, it cannot be
- even, or
- end with the digit 5.
Certain odd numbers have patterns which immediately excludes itself from the prime numbers list. Some numbers include the 'divisible by 11' odd numbers which are 121, 363 and 847. Others include the 'triple' numbers such as 111,333,555, 777 and 999.
We have shortened the list of possible prime numbers by another 8, bringing it down to 352 odd numbers left to consider.
Sequential-pattern numbers like 123, 567, 987, 321 and 789, or even 357, 753 or 147, 741 & 369, are always divisible by 3.
Another set which cannot be prime numbers are if each of the three digits in the 3-digit number is divisible by 3, such as 339, 663, 660 and 993. This brings the prime-number pool down even further.
Furthermore, if you are good with your 3- or 7- times table, doing division should be a breeze, and hence, if given an odd 3-digit which do not fall in any of the above categories, you are able to narrow down the list of possible prime numbers further by doing quick mental division using 3 or 7 which would not be a prime number if it leaves no remainder.
Now, the next step which has an increased complexity involves division with double-digit numbers, which is indeed much more difficult to do compared with single-digit numbers. However, based on the primality test, a number n can be tested for primality (the characteristic of being a prime number) by dividing using all possible numbers up to the number √n.
For example, the number 391. No single digit odd number can divide this number perfectly. Hence, we must try double-digit numbers from the number 13 (ignore using 11 as 391 is definitely not a product of 11). To test for primality, we need only use the odd prime numbers 13, 17, 19, etc. up till √n, or √391 in this case. But of course, it would defeat the purpose of using mental arithmetic if one uses a calculator to compute √391 and thus we would be at a loss. However, we can use approximation to find the value of √391, in which the closest perfect square to 391 is 400, which has a square root of 20. Hence, we need only use 13, 17 or 19 to determine if 391 is a prime number or not.
Yes, this indeed seems complex. By the way, as it turns out, 391 is a product of 17 x 23, hence NOT a prime number.
Ok, brain is in knots now you may say. :S !!!
The point of all this is to illustrate how few numbers there are in the pool of 3-digit prime numbers. The exact total is actually a mere 143 prime numbers, which is moderately easy to commit to memory.
Which brings me back to the point I was trying to make at the start of this post, that is I merely memorised a pool of 143 prime numbers; this is how I can instantly tell you if it is a prime number or not.
Now, not all that impressive anymore, ain't it? Haha.
Why I so long-winded must write so long just to say my 'talent' not very interesting after all, LOL.
But some historical fact about me regarding this 'prime number talent' is that it all started on a school bus, as a little girl on her way to school. She was always the earliest to be picked up and the last to be dropped off, hence having ample time doing nothing while on her commute to and from school. This little girl eventually learnt how to multiply and divide, opening up more 'mathematical' possibilities, which was harnessed during her commute to school. To dispel boredom on these dreaded long rides to and from school, she found that you could play arithmetic games using car number plates which can be seen everywhere while on the bus.
This is how that little girl (me) learnt and eventually memorising 3-digit numbers, whether prime number or not, and even 3-digit perfect squares.
Oh well, I guess I can still impress those who regard prime numbers as 'foreign' and 'hard to figure out' (and those who haven't read this post) !!!!