

Rutgers Graduate Student Finds New Prime-Generating Formula - jlhamilton
http://recursed.blogspot.com/2008/07/rutgers-graduate-student-finds-new.html

======
programnature
The summer school where this was conjectured was
[http://www.wolframscience.com/summerschool/2003/participants...](http://www.wolframscience.com/summerschool/2003/participants/)

As one of the "live experiments" Stephen Wolfram decided to try to find the
minimal recursive functions involving arithmetic type operations that produce
complex behavior. The article glosses over this, but no one set out to find a
function that produced only primes; it just so happened that when enumerating
these minimal functions this one was discovered to have a peculiar regularity.

By the way, if you ever discover an efficient way to generate primes, you have
a shot at claiming a 100k prize (<http://www.eff.org/awards/coop>)

------
henning
Off-topic, but it's interesting how he's reimplemented a substantial fraction
of Haskell's Prelude (base library) in Mathematica, probably without knowing
it: <http://www.math.rutgers.edu/~erowland/programs/ListTricks.m>.

------
huhtenberg
The formula (or rather the algorithm) is interesting, but rather impractical.
First million of iterations generate only 36 primes, and these are not even
sequential:

    
    
      3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 47, 53, 
      101, 127, 163, 199, 233, 421, 443, 467, 577, 941, 
      1889, 3779, 7559, 15131, 30323, 60647, 121403, 
      242807, 486041, 972533, 1945649, 3891467, 7783541

------
carterschonwald
the caveat being that the complexity of computing the formula is at best on
the order of preexisting techniques, so nifty deep math, but nothing new from
a computational point of view (barring more insight happening)

~~~
DaniFong
Since it's a new approach, it's more likely to lead to a better eventual
complexity than some technique that's already been milked for all it's worth.

Stay upstream.

~~~
Tichy
I just looked at the article again (blog article, not maths), and I must admit
the gcd in the equation does not make it seem so exciting. gcd seems
algorithmically very close to other algorithms for computing primes.

On the other hand, playing around with it would probably be fun :-/

------
lg
Man, I went to Rutgers, but it sounds like I picked the wrong major. One of my
CS TA's literally did not know what the head and tail of a list are (an
American, by the by). And to think, math was just across the hall..

~~~
yummyfajitas
I was an RU math TA. Most of us are not as smart as Eric.

~~~
andreyf
Might be, but the two departments are very different in quality also, at least
on the undergrad level (I majored in Math/CS at Rutgers).

This is mostly due to the different nature of the subjects, though - CS
enrollment fluctuates hugely with tech fashions, and includes people looking
to get ahead in their job, people learning "how computers work", etc. Math, on
the other hand, can stay to a more strictly academic curriculum, especially
with their honors track.

I forget where I read this (I think something of Alan Kay's), but I like the
thought that CS will go the path of biology, on the undergrad level, by
breaking up into several fields. Just as "pure" biology majors are separate
from the school of pharmacy, "pure" CS majors needs a different focus than
future network technicians and Blub programmers.

~~~
turkishrevenge
It really depends. The theory classes are there, you just have to take them.
My Discrete II & Algorithmic Analysis class with Professor Kalantari was great
and and extremely informative. Other classes that I thought were really
interesting, like Compilers and Formal Language and Automata theory sadly only
had a few students enrolled. I guess theoretical classes are considered
boring, although I guess I could see why others think that when compared to
Computer Graphics or something that seems a little more hands on. Now that I'm
out though, I do regret not going down the Math/CS route at Rutgers.

~~~
lg
Those "unpopular" classes like Formal Languages might not be so unpopular if
serious profs taught them, instead of the usual lazy, disorganized people who
outsource teaching to the TA's. Maybe some people make a point of avoiding the
hard profs, but _more_ people avoid the terrible ones.

------
Tichy
I have also developed a Formula that generates only 1 and primes:

    
    
      a(n) = 1

~~~
0x44
I think there might be a bug there, somewhere. I ran it here, and got 4.

~~~
chengmi
You must be using Ruby... ;)

------
hugh
Anyone know whether it's been proven that the formula will generate an
infinite number of primes? Or might it start looping back on itself
eventually?

