GIMPS Project Discovers Largest Known Prime Number • Hacker News Board

Re: GIMPS Project Discovers Largest Known Prime Number

#111

Post by [deleted] » Fri, Jan 05, 2018, 9:05 PM UTC

JackFr wrote: post #105

xamuel wrote: post #42

Earlier quoted context omitted.

When philosophers study mankind's knowledge, it's more typical to study the things mankind would ideally know at the end of all time assuming mankind could continue forever. (Formally: the knowledge predicate is usually assumed to satisfy modus ponens: if mankind knows "A implies B" and mankind knows "A", then mankind knows "B") Under this abstraction, if mankind knows the axioms of logic and Peano arithmetic, then m…

> then mankind [ideally eventually] knows the primality of all primes We already know the primality of all primes. They're prime. All numbers though . . .

[deleted]

Re: GIMPS Project Discovers Largest Known Prime Number

#112

Post by TheRealPomax » Sun, Jan 07, 2018, 4:19 PM UTC

netcraft wrote: post #15

so I didn't know this, but got curious about how many known prime there are - I knew there were infinite primes, but thought that there would be some concrete list of all the primes that we had discovered somewhere - but apparently not https://math.stackexchange.com/questions/272791/how-many-pri... > Nobody's really keeping count. ... There are very many hundred-digit primes to find. We could cover the Earth in hardd…

That list would be as long as the list of "all even numbers" because any list of primes immediately gives you a next prime that should be on the list, but isn't, in the same way that having a list of even numbers immediately gives you the next even number that should be on that list but isn't:

Given an ordered list of primes {2,3,5,...,n} one (of several) immediately known next prime number is simply (2 x 3 x 5 x ... x n) + 1. We know that number's prime because it cannot be cleanly divided by 2, or 3, or 5, or ..., or n.

As such, even if it might be useful to have a list of all known primes, annotated with what kind of prime each number is, such a list cannot be constructed: even just the subset of all prime numbers generated based on the simple above rule would be infinitely long, just like the list of all even numbers is infinitely long.

Re: GIMPS Project Discovers Largest Known Prime Number

#113

Post by dghughes » Sun, Jan 07, 2018, 9:10 PM UTC

sidhack wrote: post #43

dghughes wrote: post #41

Prime numbers are amazing. I was watching a math documentary and one example was a Cicada in North Carolina that only emerges once every thirteen years millions of them at once. It's a defense mechanism the sheer number overwhelms predators. The Cicada does this also to avoid appearing when another species of Cicada appears to prevent cross breeding. The other species in the same region emerges every 7 years. The two…

Is this the 3-part BBC documentary - "The Code"?

Yes I think that's what it is.

Re: GIMPS Project Discovers Largest Known Prime Number

#114

Post by thomasahle » Tue, Jan 09, 2018, 12:05 AM UTC

kristianp wrote: post #75

thomasahle wrote: post #67

Earlier quoted context omitted.

One application is that it's fairly cheap to take `n mod p` when `p` is on the form $2^q-1$. In particular x ≡ x mod 2^q + ⌊x/2^q⌋ (mod p). If you are making a hash function, and need to take mod a prime, this is useful. Another application of slightly larger Mersennes is https://en.wikipedia.org/wiki/Mersenne_Twister

I imagine these record-breaking primes are too large to be useful in a hash function though.

Certainly. These are just for fun, or maybe in the future giving some motivation for some number theory conjectures. Who knows.

Re: GIMPS Project Discovers Largest Known Prime Number

#115

Post by masterdev8 » Mon, Jan 15, 2018, 5:52 AM UTC

Is there a web service where you can buy a large number with certain length? Not a Mersenne prime, but just a number and/or a prime?

It needs to comply with the 2^n-1 formula. Let's say I want a number long 100 000 000 or even 1 000 000 000 long. Or a prime above that length.

Do you know how much would that cost per number prime and non-prime?