Is the Prime Spiral an Intriguing Study or Just a Quirk?

[Helical]

I've was reading about it [http://mathworld.wolfram.com/PrimeSpiral.htm] and found it intriguing, has there been a great deal of study devoted to it or is it thought of as some kind of quark?

[P.S. I don't really know much about number theory, just curious]

 

[CRGreathouse]

I think it's fairly well-understood. The diagonals are related to prime-generating polynomials (which you can also read about on MathWorld).

 

[mhill]

but ALL the diagonals of Ulam spiral generate Polynomials that have prime values or only a few special diagonals of Ulam spiral only generate primes.

 

[ramsey2879]

but ALL the diagonals of Ulam spiral generate Polynomials that have prime values or only a few special diagonals of Ulam spiral only generate primes.

Be careful, no polynomial generates only primes indefinitely. I think you meant --only generate primes up to a large value of n --!

 

[mhill]

Uh.. sorry , then i meant what are the diagonals that generate primes up to a large value of 'n' or perhaps a bit harder , given a certain prime what is the Polynomial in Ulam Spiral that for a certain integer the Polynomial gives you the prime 'p' are there SERIOUS studies with calculations for Ulam spiral.

 

[CRGreathouse]

I'm working through that one, give me a bit.Parse tree:

(Uh.. sorry)
(then i meant
 (
  (
   (
    what are the diagonals
    (that generate primes up to a large value of 'n')
   )
  or perhaps a bit harder ,
   (
    (
     (given a certain prime)
    what is the Polynomial in Ulam Spiral
     (
      (that for a certain integer)
      the Polynomial gives you the prime 'p'
     )
    )
   )
  )
 are there SERIOUS studies with calculations for Ulam spiral.)
)

Semantic re-formation:

Are there serious computational studies addressing:
1. What diagonals generate only primes up to large values of n?
2. Harder: given a prime p, what polynomials P have P(n) = p for some n?

Answer:

There are studies addressing #1. There is a close relationship between prime-generating polynomials and such serious topics as Heegner numbers (about which I know little). UPNT and MathWorld have lots of references.

#2 does not seem difficult. Do you have more conditions, or have I perhaps misunderstood you?