3 ms·

Also interesting work on twin primes this week: http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989 http://www.natu

by ximeng 13y ago

Also interesting work on twin primes this week: http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989 http://www.nature.com/news/first-proof-that-infinitely-many-...

sold 13y ago
Terence Tao's post https://plus.google.com/114134834346472219368/posts/XESxA9bL5um https://plus.google.com/114134834346472219368/posts/XESxA9bL... However, in absence of a preprint, it's IMO too soon to make announcements.
- Zenst 13y ago
  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 :-).
  - dEnigma 13y ago
    "the largest prime closest to infinity" What do you even mean by that?
    - Zenst 13y ago
      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.
      - jhart3333 13y ago
        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.
        Zenst 13y ago
        The largest known prime I was refering too was what is known now - http://en.wikipedia.org/wiki/Largest_known_prime_number 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.
        jhart3333 13y ago
        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 http://www.jimloy.com/number/primes.htm
  - shawnz 13y ago
    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).
    - scarmig 13y ago
      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.
      - sold 13y ago
        You are correct, normality is a stronger criterion. See http://en.wikipedia.org/wiki/Disjunctive_sequence http://en.wikipedia.org/wiki/Disjunctive_sequence
      - deleted 13y ago
        [deleted]
    - Zenst 13y ago
      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.
mixmax 13y ago
In my country social security numbers consist of two numbers, and mine consists of two twin primes. Probably the only one in the country. This is something I can only brag about on HN :-)
- otibom 13y ago
  Finding mixmax's country of residence, social security number, name and address is left as an exercise for the reader :)
  - mixmax 13y ago
    should definitely be doable - but using it to defraud me would be hard. Here social security numbers are used as an identifier, you can't really get to anything interesting with it. For that you'll need my passport, drivers license, digital ID or something similar. You can probably go to the doctor and claim to be me, but that's about it. As a matter of fact a popular singer once published an album where the title was his social security number to show that you can't do much with it.
- tomjen3 13y ago
  As long as we are on the subject of primes, my parents telephone number is prime (and in Denmark telephone numbers are 8 digits). WTF is the odds of that?
  - benjamincburns 13y ago
    If my math is to be believed, 5096876/90000000 or ~0.056632; roughly 1 in 20. Edit: Here's my program: http://pastebin.com/sBsXjPt5 http://pastebin.com/sBsXjPt5 Usage: gcc primes.c -O2 -o primes; ./primes 8 | wc -l Edit 2: Nevermind; I'm dumb. First, there are 10^8 unique 8 digit combos, not 10^8-10^7. If all combinations were legal we'd have a probability of 0.05096876. But I assume all combinations are not legal, so that answer too is wrong. Maybe later if I'm bored and have more time I'll research the Danish telephone system and get an accurate number.
    - 13y ago

by ximeng 13y ago

sold 13y ago

Terence Tao's post https://plus.google.com/114134834346472219368/posts/XESxA9bL5um https://plus.google.com/114134834346472219368/posts/XESxA9bL... However, in absence of a preprint, it's IMO too soon to make announcements.

Zenst 13y ago
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 :-).
- dEnigma 13y ago
  "the largest prime closest to infinity" What do you even mean by that?
  - Zenst 13y ago
    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.
    - jhart3333 13y ago
      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.
      - Zenst 13y ago
        The largest known prime I was refering too was what is known now - http://en.wikipedia.org/wiki/Largest_known_prime_number 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.
        jhart3333 13y ago
        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 http://www.jimloy.com/number/primes.htm
- shawnz 13y ago
  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).
  - scarmig 13y ago
    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.
    - sold 13y ago
      You are correct, normality is a stronger criterion. See http://en.wikipedia.org/wiki/Disjunctive_sequence http://en.wikipedia.org/wiki/Disjunctive_sequence
    - deleted 13y ago
      [deleted]
  - Zenst 13y ago
    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.

mixmax 13y ago

In my country social security numbers consist of two numbers, and mine consists of two twin primes. Probably the only one in the country. This is something I can only brag about on HN :-)

otibom 13y ago
Finding mixmax's country of residence, social security number, name and address is left as an exercise for the reader :)
- mixmax 13y ago
  should definitely be doable - but using it to defraud me would be hard. Here social security numbers are used as an identifier, you can't really get to anything interesting with it. For that you'll need my passport, drivers license, digital ID or something similar. You can probably go to the doctor and claim to be me, but that's about it. As a matter of fact a popular singer once published an album where the title was his social security number to show that you can't do much with it.
tomjen3 13y ago
As long as we are on the subject of primes, my parents telephone number is prime (and in Denmark telephone numbers are 8 digits). WTF is the odds of that?
- benjamincburns 13y ago
  If my math is to be believed, 5096876/90000000 or ~0.056632; roughly 1 in 20. Edit: Here's my program: http://pastebin.com/sBsXjPt5 http://pastebin.com/sBsXjPt5 Usage: gcc primes.c -O2 -o primes; ./primes 8 | wc -l Edit 2: Nevermind; I'm dumb. First, there are 10^8 unique 8 digit combos, not 10^8-10^7. If all combinations were legal we'd have a probability of 0.05096876. But I assume all combinations are not legal, so that answer too is wrong. Maybe later if I'm bored and have more time I'll research the Danish telephone system and get an accurate number.
  - 13y ago