John Selfridge

John Lewis Selfridge (February 17, 1927 in Ketchikan, Alaska – October 31, 2010 in DeKalb, Illinois), 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 (giving him an Erdős number of 1). 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 k2n + 1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. Five years later, 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 April 2017 only five of the original seventeen possibilities remain. In 1964, Selfridge and Alexander Hurwitz proved that the 14th Fermat number 2 2 14 + 1 {\displaystyle 2^{2^{14}}+1} was composite. However, their proof did not provide a factor. It was not until 2010 that the first factor of the 14th Fermat number was found. 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. Together with Paul Erdős, Selfridge solved a 250-year-old problem, proving that the product of consecutive numbers is never a power. It took them many years to find the proof and John made extensive use of computers, but the final version of the proof requires only a modest amount of computation, namely evaluating an easily computed function f(n) for 30,000 consecutive values of n. Selfridge suffered from writer's block and paid a former student to write up the result, even though it is only two pages long. As a mathematician, Selfridge w