Factorizations of Cunningham numbers with bases 13 to 99

This Report updates the tables of factorizations of a^n +- 1 for 13 < a < 100, previously published as CWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (Update 1, September 1994) and CWI Report NM-R9609 (Update 2, March 1996). A total of 951 new entries in the tables are given here. The factorizations are now complete for n < 76, and there are no composite cofactors smaller than 10^102.

[1]  P. L. Montgomery.  Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[2]  Françoise Morain.  Courbes elliptiques et tests de primalité , 1990 .

[3]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[4]  A. Atkin,et al.  ELLIPTIC CURVES AND PRIMALITY PROVING , 1993 .

[5]  H. T. Riele,et al.  Centrum Voor Wiskunde En Informatica , 1996 .

[6]  H. Riesel.  Prime numbers and computer methods for factorization (2nd ed.) , 1994 .

[7]  J. L. Selfridge,et al.  Factorizations of b[n]±1, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers , 1985 .

[8]  Herman J. J. te Riele,et al.  Factoring Integers with Large-Prime Variations of the Quadratic Sieve , 1996, Exp. Math..

[9]  Richard P. Brent,et al.  Recent Progress and Prospects for Integer Factorisation Algorithms , 2000, COCOON.

[10]  P. L. Montgomery,et al.  An FFT extension of the elliptic curve method of factorization , 1992 .

[11]  Richard P. Brent,et al.  Factorization of the tenth Fermat number , 1999, Math. Comput..

[12]  Robert D. Silverman.  The multiple polynomial quadratic sieve , 1987 .

[13]  H. Riesel.  Prime numbers and computer methods for factorization , 1985 .

[14]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[15]  H. W. Lenstra,et al.  Factoring integers with elliptic curves , 1987 .

[16]  Richard P. Brent,et al.  FACTORIZATIONS OF a n ± 1, 13 a < 100 , 1992 .

[17]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[18]  P. L. Montgomery,et al.  A survey of modern integer factorization algorithms , 1994 .

[19]  B. Murphy.  Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm , 1999 .

[20]  Richard P. Brent,et al.  On computing factors of cyclotomic polynomials , 1993, ArXiv.