Prime numbers: not so random?

[Imparcticle]

Here is a cool article about a pattern to the procession of prime numbers:

http://www.nature.com/nsu/030317/030317-13.html

Enjoy! :smile:

[Zurtex]

I could be wrong but surely this could never stand up as serious mathematics. There being an infinite number of primes trying to spot how likely differences are is surely like trying to spot how likely the digit 7 occurs in Pi in base 10...

[Imparcticle]

Well, if Reinmann decided to make a conjecture about the randomness of prime numbers, and it is taken seriously, then I am sure it is a serious kind of mathematics. Also, I believe the seriousness of a subject is subjective.

[matt grime]

As with a lot of popular science articles on mathematics it omits many details and gives a false impression. If I were a number theorist I'd be vaguely bemused at the 'hey look you guys, *physicists* can do it, why can't you' feeling in it. As anyone who knows about the recent interest in the zeta function will tell you, it is high'y unlikely that any number theory techniques extant will solve the Riemann Conjecture, and it is felt that physicists may have the most important input (quantum chaotical systems and random matrices, perhaps). This is not new or surprising. What is surprising is that Physics has had so little input in pure mathematics in the last 80 years compared to the previous few thousand.

And it is not true, in some sense, to say that the primes are not random, as we can prove a statement that says, in effect, that they are as random as you get, and that any statement that is true for a *random* (in a carefully stated sense) set of natural numbers is true of the primes.

Anyway, Zurtex, this area is an important one.

[HallsofIvy]

How carefully did you read the article? The people quoted do not claim they have found a pattern. They say they have found what looks like a pattern. They certainly do not claim to have proved that that pattern will always be true. I suspect that such a proof would be as difficult as proving all of the other possible patterns in prime numbers.