The Prime Number Trick

Using prime numbers, you can amaze your friends with a prime prediction...

 

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

Divide by 12

Without knowing which prime number your friends picked, you can still tell them:
 

There will be a remainder of 6.

 

 

For example, if you want to try the trick with the prime number 2801, here's what to 

push:

 

2801 * 2801 =
 

+ 17 =
 

/ 12 =

 

...and that's the answer! Now find a new prime number and try it.