# Ulam Spiral

## Main Question or Discussion Point

I've was reading about it [http://mathworld.wolfram.com/PrimeSpiral.htm] [Broken] 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]

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

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.

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 --!

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
Homework Helper
I'm working through that one, give me a bit.

Parse tree:

Code:
(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?