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GIMPS Project Discovers Largest Known Prime Number

mersenne.org

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Re: GIMPS Project Discovers Largest Known Prime Number

#21

Post by raverbashing »

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…

The relevant thing is not that's a prime (it's pretty trivial to find one), but a Mersenne Prime

Primality testing is not trivial at those number sizes

Re: GIMPS Project Discovers Largest Known Prime Number

#24

Post by OscarCunningham »

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…

I also used to think that there weren't very many primes. But the prime number theorem says that the number of primes less than n is about n/log(n). The function log doesn't grow very fast, so a large proportion of numbers are prime. For example the number of primes less than 10^100 is 4*10^97.

Primes are really really common.

Re: GIMPS Project Discovers Largest Known Prime Number

#25

Post by schoen »

kryptiskt wrote: post #18
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…

RSA encryption keys uses the product of two large primes, where each prime is many digits long. So many new primes are "discovered" every day.

Interestingly, those primes' primality is normally proven statistically rather than deductively. This is not really a practical issue for people using RSA, but could be a philosophical issue for someone interested in the question of how many different numbers' primality has been proven by humanity.

Re: GIMPS Project Discovers Largest Known Prime Number

#27

Post by organsnyder »

imhelpingu wrote: post #6

So that's what it's working on when it's starting up.

GIMPS = Great Internet Mersenne Prime Search. Completely unrelated (apart from similar naming) to the GIMP (GNU Image Editing Program).

Perhaps you were joking; but I'm sure others might be confused.

Re: GIMPS Project Discovers Largest Known Prime Number

#28

Post by OscarCunningham »

schoen wrote: post #25
kryptiskt wrote: post #18

Earlier quoted context omitted.

RSA encryption keys uses the product of two large primes, where each prime is many digits long. So many new primes are "discovered" every day.

Interestingly, those primes' primality is normally proven statistically rather than deductively. This is not really a practical issue for people using RSA, but could be a philosophical issue for someone interested in the question of how many different numbers' primality has been proven by humanity.

In fact if someone worked out how to crack RSA when it turned out that one of those numbers weren't prime then they would have invented a fast primality check. Which would be really cool in itself, and allow RSA to be fixed.

Re: GIMPS Project Discovers Largest Known Prime Number

#29

Post by schoen »

biot wrote: post #12
cortesoft wrote: post #8

Earlier quoted context omitted.

The link has another link to a page describing why this matters: http://primes.utm.edu/notes/faq/why.html

> Mersennes are beautiful and have some surprising applications. Unfortunately that page doesn’t elaborate on what these surprising applications are, which is itself surprising on a page that purports to answer “why”.

It automatically results in the discovery of a new perfect number. :-)

https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem

(combining two of history's greatest mathematicians with names that have confused generations of students by being pronounced very differently)

Re: GIMPS Project Discovers Largest Known Prime Number

#30

Post by zeep »

raverbashing wrote: post #21
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…

The relevant thing is not that's a prime (it's pretty trivial to find one), but a Mersenne Prime Primality testing is not trivial at those number sizes

not really, it is very hard to test any very large number for primality... this project only test numbers that satisfy the Mersenne prime definition though... 9 of the 10 known largest primes are Mersenne prime numbers probably because there is more people testing these numbers.

http://primes.utm.edu/largest.html#biggest

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