Finding HUGE Prime Numbers

In class we have been studying factors and multiples. Naturally, prime numbers arise during these discussions. It's easy to rattle off the first few prime numbers - 2, 3, 5, 7, 11, 13...

But how about when numbers become larger? 4,729 and 7,919 are both prime numbers.

179,424,691 is also a prime number.

So is 797,003,437!

How do you think these huge prime numbers are discovered?

Adam Spencer is an Australian radio host. He isn't a professional mathematician, but rather he is simply fascinated by math like many of you! One of his mathematical interests is prime numbers. In his TED Talk, Adam describes how "monster" prime numbers are discovered by mathematicians all over the world.

Why do you think "hunting" for "monster" primes is so fascinating? 

Would you be interested in helping hunt for monster primes?