I don't want to rain on anyone's math geek parade, but is there a practical use for discovering primes?
Is there any use beyond crunching giant numbers for theoretical physics and knowing a certain number can't be divided - or is this just the math geek equivalent of knowing the Baltimore Orioles had four 20-game winners in 1971?
It would certainly be nice if someone improved on the Lucas-Lehmer test, or if someone found another "pattern" that unreliably produces primes like the Mersenne numbers. So in some sense, this search encourages both of those things, although regrettably it's not been enough encouragement for a discovery to be made :-(
There might be, but yeah, that's not the main reason for searching IMO.
See http://primes.utm.edu/notes/faq/why.html, but it boils down to "something really interesting can be found along the way, primes relate to other important topics so learning about them has intrinsic value, there's some money in it (but you have a 99.9% chance of spending more than the prizes in your search... and you still won't win)".
> ...this record, which stood for 75 years, MAY stand
> forever as the largest prime found by hand calculations.
I shudder to imagine the holocaust which would have to happen before this record could be broken. Though I suppose we may find an alien species who might have found a larger prime "by hand."
It could happen (without catastrophe/aliens) if: (a) someone discovered a pattern like the Mersenne numbers which unreliably produces primes that are much larger than Mersenne numbers, and (b) someone discovers, by hand, a proof that one of these new numbers is prime. Such a discovery would be wonderful: new mathematics that could give us insight into what primes really are.
For instance, they are points in the geometric object known as the scheme over the integers.[1] The Riemann Zeta function of the Riemann Hypothesis generalizes to other schemes, and reflects their geometric properties (being vague because it's over a decade since I studied this stuff.) It is just barely in the realms of possibility that a new computationally simple way of finding large primes would also reflect something about the geometric structure of schemes over Z. (But it seems pretty damn unlikely to me.)
I didn't know why primes are considered special, apart from the basic requirement they fulfill. GP sounded like they might serve a bigger unknown purpose.
Is there any use beyond crunching giant numbers for theoretical physics and knowing a certain number can't be divided - or is this just the math geek equivalent of knowing the Baltimore Orioles had four 20-game winners in 1971?