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Comment by ximeng | Hacker News Reader

Also interesting work on twin primes this week:

http://www.nature.com/news/first-proof-that-infinitely-many-...

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 :-)

Finding mixmax's country of residence, social security number, name and address is left as an exercise for the reader :)

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.

By my math, if you're talking about Denmark, I don't think you're as unique as you think you are. There are a total of about 18 million valid Danish ID numbers (approximately 36.5k valid DDMMYY combinations * approximately 500 valid serials that meet the checksum), of which 204,099 are two twin primes. So I'd expect about 1% of the country to have two twin primes for their ID number.

So not only are you probably not the only one in the country to have two twin primes for an ID number, you're probably not the only Dane on Hacker News for whom that's true!

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?

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

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.

Alright - Denmark made it easy on me with the spreadsheet here: http://www.erhvervsstyrelsen.dk/numbering_lists

The probability that a valid, non-reserved, 8-digit danish phone number is prime is 4208056/73399100, or ~0.0573312. This probability does not account for number blocks which are valid but not yet assigned/purchased.

Code uses a copy of the number spreadsheet without header row saved as 'danish_numberlist.csv'

Code here: http://pastebin.com/kWUsHsL4

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 :-).

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.

"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

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