Mathematician:John Lewis Selfridge

Mathematician

American mathematician who contributed to the fields of analytic number theory, computational number theory and combinatorics.

Proved in $1962$ that $78 \ 557$ is a Sierpiński number of the second kind.

Conjectured (with Wacław Franciszek Sierpiński) that it is also the smallest. This still has not been proven (see Sierpiński Problem).

Nationality

American

History

• Born: February 17, 1927, Ketchikan, Alaska, United States
• Died: October 31, 2010, DeKalb, Illinois

Theorems and Definitions

• Baillie-PSW Primality Test (with Robert Baillie, Carl Bernard Pomerance and Samuel Standfield Wagstaff Jr.)
• Erdős-Selfridge Function (with Paul Erdős)

Publications

• 1953: Note $156$ -- Factors of Fermat numbers (MTAC Vol. 7: pp. 274 – 275)  www.jstor.org/stable/2002843

• 1955: E1123: Polygonal Path Covering a Square Lattice (addendum) (Amer. Math. Monthly Vol. 62: p. 443)  www.jstor.org/stable/2307008

• 1960: E1408: The Highest Power of $2$ in the Numerator of $\sum_{i = 1}^k 1 / \left({2 i - 1}\right)$ (Amer. Math. Monthly Vol. 67: pp. 924 – 925) (with D.L. Silverman)  www.jstor.org/stable/2309478

• 1974: A New Function Associated with the prime factors of $\dbinom n k$ (with E.F. Ecklund Jr. and Paul Erdős)

• 1975: Not Every Number is the Sum or Difference of Two Prime Powers (Math. Comp. Vol. 29, no. 129: pp. 79 – 81) (with Frederick R. Cohen) (in which Not Every Number is the Sum or Difference of Two Prime Powers is presented)  www.jstor.org/stable/2005463

• July 1980: The Pseudoprimes to $25 \cdot 10^9$ (Math. Comp. Vol. 35, no. 151: pp. 1003 – 1026) (with Carl Pomerance and Samuel S. Wagstaff, Jr.)  www.jstor.org/stable/2006210

• 1983: Factorizations of $b^n \pm 1$ up to high powers (Contemporary Mathematics Vol. 22: pp. 1 – 178) (with John Brillhart, D.H. Lehmer, Samuel S. Wagstaff Jr. and Bryant Tuckerman)

• 1988: Factorizations of $b^n \pm 1, b = 2, 3, 5, 6, 7, 10, 11, 12$ up to high powers (2nd ed.) (Contemporary Mathematics Vol. 22: pp. 1 – 226) (with John Brillhart, D.H. Lehmer, Samuel S. Wagstaff Jr. and Bryant Tuckerman)

• Dec. 1986: Pairs of Squares with Consecutive Digits (Math. Mag. Vol. 59, no. 5: pp. 270 – 275) (with C.B. Lacampagne)  www.jstor.org/stable/2689401

• 1993: Estimates of the Least Prime Factor of a Binomial Coefficient (with Paul Erdős and C.B. Lacampagne)