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Comment by sold | Hacker News Reader

Terence Tao's post https://plus.google.com/114134834346472219368/posts/XESxA9bL...

However, in absence of a preprint, it's IMO too soon to make announcements.

True, especialy given we don't know the largest prime closest to infinity, but whilst not a formal mathmatician (autistic) it is true. Just needs simpler explanation as anything more than a page is probably over detailed in my oppinion. But I can understand why it is as long.

Still all 133 pages already exist somewhere in Pi's infinite digits, and how many pages would it take to prove that one :-).

"the largest prime closest to infinity" What do you even mean by that?

Sorry, probably not the best way to point out that we do not know what the largest prime is as we constantly keep proving larger known primes and by that they are infinite and expressed as infinity being the largest possible ever number.

Hope that explains what I mean't by that term you quoted now.

There is no largest prime. In fact the classic proof that there are infinitely many primes starts with the assumption that there is a largest prime and proceeds to use this number to construct a larger number which is also prime. This is a contradiction: "this is the largest prime" and "this is not the largest prime." So the original assumption must be false and "there is no largest prime" or equivalently "there are infinitely many primes". Recently it has been shown that this proof is a result of misunderstanding the one given in Euclid's Elements. Nevertheless it's still a fine proof.

The largest known prime I was refering too was what is known now - http://en.wikipedia.org/wiki/Largest_known_prime_number

So given that to know with all certaintity that only upto that value three times would be the only provable maximum value, until a new know prime is found and somebody invents a formular to drop in N and get the Nth prime out without waiting more than few seconds. Currently we can not do that at all, let alone that dream of many, maybe one day in our lifetimes.

I agree, it is a fine proof. I hope to appreciete it more over the following days. Lots to go over.

It's been a while since I studied this stuff and I screwed up a crucial part of the argument. The larger number isn't guaranteed to be prime. It's either prime or composite. In either case you end up with a prime not in the finite list of primes that follow from the assumption of a largest prime. Here is a link to a good explanation that includes the composite case:

http://www.jimloy.com/number/primes.htm

We know that there are an infinite number of primes (Euclid's theorem). We don't yet know whether or not every possible sequence of data occurs in the digits of pi, but it's highly suspected (this would make pi a "normal number" if true).

Isn't a normal number ever so subtly different from that? In that not only does every possible sequence of data occur in the digits of a normal number, but each sequence occurs an infinite number of times with likelihood proportional to the number of digits.

Infinities always mix up my intuitions, though, so they might be equivalent.

You are correct, normality is a stronger criterion. See http://en.wikipedia.org/wiki/Disjunctive_sequence

True, it was one of those `gravity` moments or feelings about it perhaps -- You know it is there but still have not proven how it fully works, though my a physics aspect but I do like to think of them hand in hand. Perhaps another bias perceptional thought process, sorry my bad.

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