Prime numbers info

**OReilly** · May 18th 2006, 05:44 PM

How many prime numbers has been discovered to this day and what is at the moment highest prime number?

**ThePerfectHacker** · May 18th 2006, 06:06 PM

Originally Posted by OReilly

How many prime numbers has been discovered to this day and what is at the moment highest prime number?

Many. Hope that helps.

There is a class of primes called "Mersenne Primes" they have form $2^n-1$ . One interesting fact is that if this number is prime then $n$ must it self be prime! If I remember properly-(I might be wrong)that,
$2^{65537}-1$ is prime,
I only remember that because
$65537=2^{2^4}+1$ a Fermat prime.
I think it might be among the highest.

**CaptainBlack** · May 18th 2006, 08:33 PM

Originally Posted by ThePerfectHacker

Many. Hope that helps.

There is a class of primes called "Mersenne Primes" they have form $2^n-1$ . One interesting fact is that if this number is prime then $n$ must it self be prime! If I remember properly-(I might be wrong)that,
$2^{65537}-1$ is prime,
I only remember that because
$65537=2^{2^4}+1$ a Fermat prime.
I think it might be among the highest.

As of Dec 2005 the record holder is: $2^{30402457}-1$

RonL

**rgep** · May 18th 2006, 10:24 PM

There are many resources listed in the Open Directory Project.

Your questions are answered on The Prime Pages.

**ThePerfectHacker** · May 19th 2006, 09:32 AM

Yet no-one was able to develope a prime producing algorithm.

**topsquark** · May 20th 2006, 04:02 AM

Originally Posted by ThePerfectHacker

Yet no-one was able to develope a prime producing algorithm.

I have one, but it's too long to post here. (Actually I'm just saying that because I'm going on a trip next weekend and if I die this will give me something to be famous for!)

-Dan

**Aradesh** · May 20th 2006, 04:41 AM

Originally Posted by topsquark

I have one, but it's too long to post here. (Actually I'm just saying that because I'm going on a trip next weekend and if I die this will give me something to be famous for!)

-Dan

that was hardy's trick

or atleast he thought god would therefore not let him die, as to not let him die with posthumous fame, like fermat's last theorem.

**ThePerfectHacker** · May 20th 2006, 07:07 PM

Originally Posted by topsquark

I have one, but it's too long to post here. (Actually I'm just saying that because I'm going on a trip next weekend and if I die this will give me something to be famous for!)

-Dan

I hope you are serious.

Anyway, it cannot be a polynomial remember that.

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