# Mathematician:John Lewis Selfridge

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## 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

- 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**: 924 – 925) (with D.L. Silverman) www.jstor.org/stable/2309478

- 1974:
*A New Function Associated with the prime factors of $\displaystyle \binom n k$*(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*: 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*: 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**: 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**: 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*: 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)