Editing Ulam spiral (section)

==History==
According to Gardner, Ulam discovered the spiral in 1963 while doodling during the presentation of "a long and very boring paper" at a scientific meeting.{{sfn|Gardner|1964|p=122}}  These hand calculations amounted to "a few hundred points".  Shortly afterwards, Ulam, with collaborators Myron Stein and Mark Wells, used [[MANIAC II]] at [[Los Alamos National Laboratory|Los Alamos Scientific Laboratory]] to extend the calculation to about 100,000 points.  The group also computed the density of primes among numbers up to 10,000,000 along some of the prime-rich lines as well as along some of the prime-poor lines.  Images of the spiral up to 65,000 points were displayed on "a scope attached to the machine" and then photographed.{{sfn|Stein|Ulam|Wells|1964|p=520}}  The Ulam spiral was described in Martin Gardner's March 1964 ''Mathematical Games'' column in ''Scientific American''  and featured on the front cover of that issue.  Some of the photographs of Stein, Ulam, and Wells were reproduced in the column.

In an addendum to the ''Scientific American'' column, Gardner mentioned the earlier paper of Klauber.{{sfn|Gardner|1971|p=88}}<ref>{{citation
 | title = Guide to the Martin Gardner papers
 | last=Hartwig |first = Daniel 
 | publisher = The Online Archive of California
 | year = 2013
 | page = 117
 | url = http://www.oac.cdlib.org/findaid/ark:/13030/kt6s20356s/
}}.</ref>
Klauber describes his construction as follows, "The integers are arranged in triangular order with 1 at the apex, the second line containing numbers 2 to 4, the third 5 to 9, and so forth.  When the primes have been indicated, it is found that there are concentrations in certain vertical and diagonal lines, and amongst these the so-called Euler sequences with high concentrations of primes are discovered."{{sfn|Daus|1932|p=373}}