I just found this flying under the radar. "John Selfridge, mathematician, computer pioneer and philanthropist, 83, of DeKalb, Ill., died on Halloween, Oct. 31, 2010."
Obituary: JOHN SELFRIDGE (1927-2010)
About the Sierpinski Problem
WacÅ‚aw Franciszek SierpiÅ„ski (14 March 1882 â€” 21 October 1969), a Polish mathematician, was known for outstanding contributions to set theory, number theory, theory of functions and topology. It is in number theory where we find the Sierpinski problem.
Basically, the Sierpinski problem is "What is the smallest Sierpinski number"
First we look at Proth numbers (named after the French mathematician FranÃ§ois Proth). A Proth number is a number of the form k*2^n+1 where k is odd, n is a positive integer, and 2^n>k.
A Sierpinski number is an odd k such that the Proth number k*2^n+1 is not pri[u]me for all n. For example, 3 is not a Sierpinski number because n=2 produces a prime number (3*2^2+1=13). In 1962, John Selfridge proved that 78,557 is a Sierpinski number...meaning he showed that for all n, 78557*2^n+1 was not prime.
Most number theorists believe that 78,557 is the smallest Sierpinski number, but it hasn't yet been proven. In order to prove it is the smallest, it has to be shown that every single k less than 78,557 is not a Sierpinski number, and to do that, some n must be found that makes k*2^n+1 prime.
The smallest proven 'prime' Sierpinski number is 271,129. In order to prove it is the smallest, it has to be shown that every single 'prime' k less than 271,129 is not a Sierpinski number, and to do that, some n must be found that makes k*2^n+1 prime.
Seventeen or Bust is working on the Sierpinski problem and the Prime Sierpinski Project is working on the 'prime' Sierpinski problem. The following k's remain for each project:
Sierpinski problem 'prime' Sierpinski problem