Williams, H. C.; Shallit, J. O. Factoring integers before computers. (English) Zbl 0847.11002 Gautschi, Walter (ed.), Mathematics of computation, 1943-1993: a half-century of computational mathematics. Mathematics of computation 50th anniversary symposium, August 9-13, 1993, Vancouver, Canada. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 48, 481-531 (1994). This interesting article surveys the history of computational number theory, with a focus on primality testing and integer factoring from 1750 to 1950. The authors begin with a discussion of the early history of primality testing and the work of Charles Babbage. They then go into detail regarding the work of Lucas, Mersenne, and some of the mechanical devices that were built. Factoring is covered in detail; the authors discuss the work of D. N. Lehmer, D. H. Lehmer, Seelhoff, Pepin, Cole, Kraitchik, and many others. The bibliography is quite extensive, with 187 references.For the entire collection see [Zbl 0807.00006]. Reviewer: J.Sorenson (Indianapolis) Cited in 2 Documents MSC: 11-03 History of number theory 11Y05 Factorization 11Y11 Primality 11A51 Factorization; primality 11Y16 Number-theoretic algorithms; complexity 01A55 History of mathematics in the 19th century 01A60 History of mathematics in the 20th century 01A50 History of mathematics in the 18th century Keywords:factoring; history of computational number theory; history of primality testing; bibliography PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{J. O. Shallit}, Proc. Symp. Appl. Math. 48, 481--531 (1994; Zbl 0847.11002) Online Encyclopedia of Integer Sequences: Pseudo-squares: a(n) = the least nonsquare positive integer which is 1 mod 8 and is a (nonzero) quadratic residue modulo the first n odd primes.