Reply to: Largest known prime number found

[OwlHoot]

Was into number theory when younger. The search for big primes had just started, but conjecture at the time was that there probably was a number which after which no possible primes could exist.

You must be cogging on a bit, over 2000 years old, because Euclid proved in ancient times that there's an infinite number of primes, for the simple reason that if there were only a finite number of primes, and p_1, p_2, ... p_n was a list of all of them, then (p_1 * p_2 * ... * p_n) + 1 exceeds 1 and is thus divisible by at least one prime but is not divisible by any primes in the list, and hence must be a product of prime(s) not in the list, which contradicts the assumption that the list is complete.

(unless you are talking about primes of a certain restricted form, such as Fermat primes 2^2^n + 1 for integer n, of which is it generally believed there are only a finite number, all already found. But it is pretty safe to say that nobody believes there are only a finite number of Mersenne primes (of the form 2^p - 1 with p prime).

[clearedforlanding]

Surely its for you to prove I'm wrong?

Yes you are right. This is mathematics not religion.

Proofs are binary; a mathematical proposition is either proven (in which case it becomes a theorem) or not (in which case it remains a conjecture until it is proven). There is nothing in between. A theorem cannot be kind of proven or almost proven. These are the same as unproven.

[northernladuk]

Yeah? But can you prove it?

The set being infinite does not imply that that there are an infinite number of elements in that set that have a particular property. There's only one even prime. And the Lenstra–Pomerance–Wagstaff conjecture (that there are infinite number of Mersenne Primes) hasn't been proved.

Surely its for you to prove I'm wrong?

But isn't this it?

https://en.m.wikipedia.org/wiki/Euclid%27s_theorem

[OwlHoot]

If you are working with an infinite number of numbers there is guaranteed to be an infinite number of primes. ..

HUH?! Not necessarily - There are an infinite number of integer multiples of 6, but none of them is prime.

[BlasterBates]

http://forums.contractoruk.com/light...ml#post2198503

[pr1]

Was into number theory when younger. The search for big primes had just started, but conjecture at the time was that there probably was a number which after which no possible primes could exist.

"...could exist" - I'd disagree
"...could be found" - probably true

[NigelJK]

Was into number theory when younger. The search for big primes had just started, but conjecture at the time was that there probably was a number which after which no possible primes could exist.

[pr1]

Yeah? But can you prove it?

The set being infinite does not imply that that there are an infinite number of elements in that set that have a particular property. There's only one even prime. And the Lenstra–Pomerance–Wagstaff conjecture (that there are infinite number of Mersenne Primes) hasn't been proved.

I think it does

There's only one even prime because everything above that is divisible by that prime (it's a coincidence that that's also how we define the word "even"), yes the gaps between primes is getting exponentially bigger (hence it's increasingly harder to find the next one) but given an infinite set there must be an infinite number - the problem will be when the numbers get SO big that we lose the ability to describe them, but it doesn't mean they don't exist (remember numbers are an arbitrary human-made concept)

As for proving it - it's hard (impossible?) to prove there are infinity of something in a set of infinity but,

if you can accept there are infinity numbers
and you can accept there are infinity odd numbers
and you can accept there are infinity numbers divisible by 3

Then it's the same logic for primes!

[mudskipper]

Please don't post a teaser like that.
You need to include the number in this thread so we can admire it in all its glory.

It has its own wikipedia page, but they've omitted a few digits

https://en.wikipedia.org/wiki/Larges...n_prime_number

[ctdctd]

Largest known prime number discovered in Missouri - BBC News

I didn't know it was lost - was it behind the sofa?

Please don't post a teaser like that.
You need to include the number in this thread so we can admire it in all its glory.

[NotAllThere]

If you are working with an infinite number of numbers there is guaranteed to be an infinite number of primes. That's the interesting thing about the term infinite that most of us can't comprehend.

Yeah? But can you prove it?

The set being infinite does not imply that that there are an infinite number of elements in that set that have a particular property. There's only one even prime. And the Lenstra–Pomerance–Wagstaff conjecture (that there are infinite number of Mersenne Primes) hasn't been proved.

[SlipTheJab]

Not yet. It's a bit too big for our current technology.

Granted but we'll soon need the strength (NSA back doors not withstanding!)

[clearedforlanding]

Thanks for stating the obvious Einstein but the real story here is that knowing the current largest provides for extra leverage in areas such as security and specifically cryptography

Not yet. It's a bit too big for our current technology.

[SlipTheJab]

If you are working with an infinite number of numbers there is guaranteed to be an infinite number of primes. That's the interesting thing about the term infinite that most of us can't comprehend.

Thanks for stating the obvious Einstein but the real story here is that knowing the current largest provides for extra leverage in areas such as security and specifically cryptography

[AtW]

Largest known prime number discovered in Missouri - BBC News

I didn't know it was lost - was it behind the sofa?

Not mine...