Prime numbers: How high can you go?

[mynah]

Not my field of expertise, but I've always wondered. Seems that new boundaries have been set with a 13 million digit number.

 

Is there any way of determining the highest possible prime number? A grade 12 student from South Africa is said to have surprised experts with an algorithm for calculating primes.

[Turtle]

Not my field of expertise, but I've always wondered. Seems that new boundaries have been set with a 13 million digit number.

 

Is there any way of determining the highest possible prime number? A grade 12 student from South Africa is said to have surprised experts with an algorithm for calculating primes.

 

No way to find a 'highest' prime, or 'highest' member of any infinite set. The periodic reports of boundary breaking have to do with increased computer power combined with short-cut algorithms.

 

Here's an interesting algorithm that Craig devised for finding Primes. :hyper: >> PRMP - an algorithm for generating the primes using only “+1” and “=”

[Nootropic]

No way to find a 'highest' prime, or 'highest' member of any infinite set

 

That's almost correct. If we consider the set of all t in in the real numbers such that t^2 is less than or equal to the square root of 2, than this set is clearly infinite and does have a maximum at square root of 2. Statements such as these are made more precise in the language of supremum and infimum.

 

Euclid gave the first (and very elegant) proof that there are infinitely many primes. There are others, such as Zariski's proof that utilize topology.

[Turtle]

That's almost correct. If we consider the set of all t in in the real numbers such that t^2 is less than or equal to the square root of 2, than this set is clearly infinite and does have a maximum at square root of 2. Statements such as these are made more precise in the language of supremum and infimum.

 

Euclid gave the first (and very elegant) proof that there are infinitely many primes. There are others, such as Zariski's proof that utilize topology.

 

Or, is it correct only in so far as it goes. ;) :) No sense messing with Euclid though; I agree. Relatively elegant is, as elegant did.

[Nootropic]

well, there's infinite sets that are bounded and then there's infinite sets that are not bounded. And then there's talk of bounded below and above, you can see that both my set and the integers are not bounded below, but that my set is bounded above but the integers are not bounded above.