John Selfridge

Who is John Selfridge?

John Lewis Selfridge, was an American mathematician who contributed to the fields of analytic number theory, computational number theory, and combinatorics. He co-authored 14 papers with Paul Erdős.

Selfridge received his Ph.D. in 1958 from the University of California, Los Angeles under the supervision of Theodore Motzkin.

In 1962, he proved that 78,557 is a Sierpinski number; he showed that, when k=78,557, all numbers of the form k2 + 1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. Five years after, he and Sierpiński proposed the conjecture that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem. A distributed computing project called Seventeen or Bust is currently trying to prove this statement, as of January 2011 only six of the original seventeen possibilities remain.

In 1975 John Brillhart, Derrick Henry Lehmer and Selfridge developed a method of proving the primality of p given only partial factorizations of p − 1 and p + 1. Together with Samuel Wagstaff they also all participated in the Cunningham project.