John Selfridge
John Selfridge | |
---|---|
Born | University of Illinois at Urbana-Champaign Northern Illinois University | February 17, 1927
Doctoral advisor | Theodore Motzkin |
John Lewis Selfridge (February 17, 1927 – October 31, 2010[1]), was an American mathematician who contributed to the fields of analytic number theory, computational number theory, and combinatorics.
Education
Selfridge received his Ph.D. in 1958 from the University of California, Los Angeles under the supervision of Theodore Motzkin.[2]
Career
Selfridge served on the faculties of the
Research
In 1962, he proved that 78,557 is a
In 1964, Selfridge and Alexander Hurwitz proved that the 14th Fermat number was composite. [5] However, their proof did not provide a factor. It was not until 2010 that the first factor of the 14th Fermat number was found. [6] [7]
In 1975
Together with Paul Erdős, Selfridge solved a 150-year-old problem, proving that the product of consecutive numbers is never a power.[9] 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 thanked "R. B. Eggleton for reorganizing and writing the paper in its final form".[9]
Selfridge also developed the
Selfridge's conjecture about Fermat numbers
Selfridge made the following conjecture about the
Selfridge's conjecture about primality testing
This conjecture is also called the PSW conjecture, after Selfridge,
Let p be an odd number, with p ≡ ± 2 (mod 5). Selfridge conjectured that if
- 2p−1 ≡ 1 (mod p) and at the same time
- fp+1 ≡ 0 (mod p),
where fk is the kth
See also
- Sierpinski number
- New Mersenne conjecture
- Lander, Parkin, and Selfridge conjecture
- Erdős–Selfridge function at Wolfram MathWorld
References
- ^ a b "John Selfridge (1927–2010)". DeKalb Daily Chronicle. November 11, 2010. Retrieved November 13, 2010.
- ^ John Selfridge at the Mathematics Genealogy Project
- ^ "Chinese Acrobatics, an Old-Time Brewery, and the "Much Needed Gap": The Life of Mathematical Reviews" (PDF). ams.org. 1997-03-01. Retrieved 2023-05-04.
- ^ "Math Times, Fall 2007". Archived from the original on 2011-06-05.
- JSTOR 2003419.
- ^ Rajala, Tapio (3 February 2010). "GIMPS' second Fermat factor!". Retrieved 9 April 2017.
- ^ Keller, Wilfrid. "Fermat factoring status". Retrieved 11 April 2017.
- JSTOR 2005583.
- ^ ISSN 0019-2082.
- ^ Prime Numbers: A Computational Perspective, Richard Crandall and Carl Pomerance, Second edition, Springer, 2011 Look up Selfridge's Conjecture in the Index.
- ^ According to an email from Pomerance.
- ^ Carl Pomerance, Richard Crandall, Prime Numbers: A Computational Perspective, Second Edition, p. 168, Springer Verlag, 2005.
Publications
- Pirani, F. A. E.; Moser, Leo; Selfridge, John (1950). "Elementary Problems and Solutions: Solutions: E903". Am. Math. Mon. 57 (8): 561–562. MR 1527674.
- JSTOR 2006210.
- Eggan, L. C.; Eggan, Peter C.; Selfridge, J. L. (1982). "Polygonal products of polygonal numbers and the Pell equation". MR 0660755.
- Erdos, P; Selfridge, J. L. (1982). "Another property of 239 and some related questions". Congr. Numer.: 243–257. MR 0681710.
- S2CID 120373455.
- MR 0868804.
- Blair, W. D.; MR 1540993.
- Guy, R. K.; Lacampagne, C. B.; Selfridge, J. L. (1987). "Primes at a glance". Math. Comput. 48 (177): 183–202. MR 0866108.
- Trench, William F.; Rodriguez, R. S.; Sherwood, H.; MR 1541238.
- Erdos, P.; Lacampagne, C. B.; Selfridge, J. L. (1988). "Prime factors of binomial coefficients and related problems". Acta Arith. 49 (5): 507–523. MR 0967334.
- Bateman, P. T.; Selfridge, J. L.; Wagstaff, S. S. (1989). "The New Mersenne conjecture". Am. Math. Mon. 96 (2): 125–128. MR 0992073.
- Lacampagne, C. B.; Nicol, C. A.; Selfridge, J. L. (1990). "Sets with nonsquarefree sums". Number Theory. de Gruyter. pp. 299–311.
- Howie, John M.; Selfridge, J. L. (1991). "A semigroup embedding problem and an arithmetical function". Math. Proc. Camb. Philos. Soc. 109 (2): 277–286. S2CID 120671857.
- Eggleton, R. B.; Lacampagne, C. B.; Selfridge, J. L. (1992). "Eulidean quadratic fields". Am. Math. Mon. 99 (9): 829–837. MR 1191702.
- Erdos, P.; Lacampagne, C. B.; Selfridge, J. L. (1993). "Estimates of the least prime factor of a binomial coefficient". Math. Comput. 61 (203): 215–224. MR 1199990.
- Lin, Cantian; Selfridge, J. L.; Shiue, Peter Jau-shyong (1995). "A note on periodic complementary binary sequences". J. Comb. Math. Comb. Comput. 19: 225–29. MR 1358509.
- Blecksmith, Richard; McCallum, Michael; Selfridge, J. L. (1998). "3-smooth representations of integers". Am. Math. Mon. 105 (6): 529–543. MR 1626189.
- Blecksmith, Richard; Erdos, Paul; Selfridge, J. L. (1999). "cluster primes". Am. Math. Mon. 106 (1): 43–48. MR 1674129.
- Erdos, Paul; Malouf, Janice L.; Selfridge, J. L.; Szekeres, Esther (1999). "Subsets of an interval whose product is a power". Discrete Math. 200 (1–3): 137–147. MR 1692286.
- Granville, Andrew; Selfridge, J. L. (2001). "Product of integers in an interval, modulo squares". Electron. J. Comb. 8 (1): #R5. MR 1814512.