Interesting properties of Prime Numbers

A Prime Number is a natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) greater than 1 that has no positive divisors other than 1 and itself.

A natural number greater than 1 that is not a prime number is called a composite number.

For example, 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6.

The square of prime number & 6 mystery!

If you square ANY prime number bigger than 5, then add 17 to it and then divide the result by 12, there will always be a remainder of 6!
For example, if you want to try the trick with the prime number 37, here's what to push:

372 => 1369 + 17 => 1386 / 12 => 115, with a remainder 6.
If you want to try with the prime number 2801, here's what to push:
28012 = + 17 = / 12 =
...and that's the answer! Now find a new prime number and try it.

The square of prime number & 9 mystery!

If you square ANY prime number greater than 3, then subtract 4, then divide the new result by 12 and the remainder is always 9.

For example, if you want to try the trick with the prime number 37, here's what to push:
372 => 1369 - 4 => 1365 / 12 => 113, with a remainder 9.

The square of prime number & 24 mystery!

If you square ANY prime number bigger than 3, then subtract 1, the answer always divides by 24!

For example,
372 => 1369 - 1 => 1368 and yes 1368 does divide by 24.
112 = 121 then 121 - 1 = 120 and yes 120 does divide by 24.

The Prime Number Trick!

Now you can have games with your friends and fellows with the above properties of prime number.

As for instance, ask your friends to pick any prime number bigger than 5, but they must not tell you what it is.
Square it. (In other words multiply the prime number by itself.)
Add 17 and then Divide by 12.

Without knowing which prime number your friends picked, you can still tell them: There will be a remainder of 6.

… You can have games with other 2 properties as well…