A sieve method for factoring numbers of the form

Author:
Daniel Shanks

Journal:
Math. Comp. **13** (1959), 78-86

MSC:
Primary 65.00; Secondary 10.00

DOI:
https://doi.org/10.1090/S0025-5718-1959-0105784-2

MathSciNet review:
0105784

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**[1]**L. E. Dickson,*History of the Theory of Numbers*, Stechert, New York, 1934, v. 1, Ch. XVI. For example, Euler (1752) gave See also D.H. Lehmer,*Guide to Tables in the Theory of Numbers*, National Research Council, Washington, D. C., 1941, p. 31-32 and p. 45.**[2]**The most extensive table of all the prime factors of ( up to ) is the unpublished table of J. W. Wrench, Jr. See UMT 1,*MTAC*, v. I, 1943, p. 26. Recently a 704 program by the author in collaboration with Dr. Wrench raised this limit to 50,000 for a table of the*greatest*prime factor. However, we now consider that type of program (with trial divisions) to be superseded by the present sieve method.**[3]**G. H. Hardy & J. E. Littlewood, ``Partitio numerorum III: On the expression of a number as a sum of primes,''*Acta Math.*, v. XLIV, 1923, p. 48.**[4]**A. E. Western, ``Note on the number of primes of the form ,'' Cambridge Phil. Soc.,*Proc.*, v. XXI, 1922, p. 108-109. Western assumes following Cunningham, who omits . The correct value of is 1200.**[5]***Fortune*, June, 1958, p. 140.**[6]**John Todd, ``A problem on arc tangent relations,''*American Math Monthly*, v. LVI, 1949, p. 517-528. MR**0031496 (11:159d)****[7]**S. D. Chowla & J. Todd, ``The density of reducible integers,''*Canadian Jour. of Math*, v. I, 1949, p. 297-299. The table of to has many errors. It indicates . A mimeographed errata sheet later circulated stated , but the correct value is 1467. MR**0030558 (11:14d)****[8]**John Todd,*Table of Arctangents of Rational Numbers*, NBS, Applied Math. Series 11, Washington, D. C., 1951. MR**0040796 (12:750e)****[10]**C. C. MacDuffee,*An Introduction to Abstract Algebra*, Wiley, New York, 1940, p. 193-202. MR**0003591 (2:241b)**

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DOI:
https://doi.org/10.1090/S0025-5718-1959-0105784-2

Article copyright:
© Copyright 1959
American Mathematical Society