# Ulam's spiral

See Wikipedia. Extract from Wikipedia below.

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by
mathematician StanisÅ‚aw Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in
Scientific American a short time later.It is constructed by writing the positive integers in a square
spiral and specially marking the prime numbers.

Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial ${x}^{2}-x+41$ , are believed to produce a high density of prime numbers.Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has ever been proved to generate infinitely many primes, much less to have a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be.

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