The Largest Known Prime by Year: A Brief History | Hacker News Reader

The Largest Known Prime by Year: A Brief History

primes.utm.edu

71 pointsvgnet21 comments

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)".

"Public key crypto algorithms utilize prime numbers extensively; indeed, prime numbers are an essential part of the major public key systems" http://www.sans.org/reading_room/whitepapers/vpns/prime-numb...

but they cannot use "biggest" primes because, typically, security relies on the prime being unknown.

Yes. But they employ techniques that were at the forefront of the search for big prime numbers in earlier times.

Is that how cracking begins? They start with "famously" prime numbers? I've always wondered about this.

  > ...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.

https://en.wikipedia.org/wiki/Double_Mersenne_number might be one place to start.

I'd like to understand why primes are believed to be really something, can you please elaborate?

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.)

[1] http://en.wikipedia.org/wiki/Scheme_(mathematics)#Modern_def...

Sorry, could you please clarify your question?

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.

A study of number theory will enlighten you. By the way, 2 is most special prime. Lots of nice theorems about prime numbers have special cases for 2.

We haven't seen a prime larger than M43112609 since 2008. What gives?

This page claims to have been last updated 21 April 2012, http://primes.utm.edu/largest.html

As tectonic links, Wolfram Alpha gives the same result.

I'm not sure why we haven't found any more lately though, but the information seems to be correct.

The wikipedia page is interesting. We have discovered new large primes since 2008, they just haven't been bigger.

https://en.wikipedia.org/wiki/Largest_known_prime_number

I wonder how long it would take running the prime number shitting bear to discover a new prime...? http://alpha61.com/primenumbershittingbear/

What do you mean by `new'? A prime that hasn't been seen by any human? Or a new largest prime?

I imagine you'd hit the integer limit, first.

WolframAlpha: http://www.wolframalpha.com/input/?i=largest+known+prime

Reply on news.ycombinator.com