Prime number in spotlight again

News! Largest prime number found! 17 MILLION digits. Details in here. I don't know how much paper needed to even write this number down. Yes, this is perhaps useless information. Once upon a time, I took a Number Theory class so I have heard of Mersenne primes. During that quarter, I even understood some of the theorems involving them listed here.

Now as the Time article says, there are infinitely number of primes out there so this would be a never ending task. Euclid! This important guy wrote the classic geometry text Elements that included this famous proof. That proof-by-contradiction demonstrates the elegant nature of pure logical argument. If you have not seen it you do not have a clue what mathematics is about. People who think math is just calculation drills are extremely shallow.

See here for example, for a write up of Euclid's proof. Got it? (Ok, this is listed in High School category, yikes I didn't learn this until college)

What makes math hard for many folks is that the (formal) language is kinda cryptic... That link above actually says it pretty well. If you still don't get it, let ME try:

Ok, suppose there are finitely many primes. We label them p1, p2,... pn. Now, multiply them all up and add 1 to it.
Is this number a prime? No, because all the primes were used so it can't be prime.
Is this number a composite? No, because none of the n identified primes would divide into it evenly, there is that 1 remainder.
See, we get in to a difficult situation so the original assumption of finitely many primes is wrong and therefore there must be infinitely many primes.