Sacks spiral

Robert Sacks devised the Sacks spiral, a variant of the Ulam spiral, in 1994. It differs from Ulam's in three ways: it places points on an Archimedean spiral rather than the square spiral used by Ulam, it places zero in the center of the spiral, and it makes a full rotation for each perfect square while the Ulam spiral places two squares per rotation. Certain curves originating from the origin appear to be unusually dense in prime numbers; one such curve, for instance, contains the numbers of the form "n"² + "n" + 41, a famous prime-rich polynomial discovered by Leonhard Euler in 1774. The extent to which the number spiral's curves are predictive of large primes and composites remains unknown.

A closely related spiral, described by harvtxt|Hahn|2008, places each integer at a distance from the origin equal to its square root, at a unit distance from the previous integer. It also approximates an Archimedean spiral, but it makes less than one rotation for every three squares.

References

*citation|last=Hahn|first=Harry K.|title=The distribution of prime numbers on the square root spiral|year=2008|id=arxiv|0801.1441.

External links

* [http://www.numberspiral.com Robert Sacks' web site]
* [http://naturalnumbers.org/sparticle.html Article about the Sacks Number Spiral]