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Abstract: As an extension of the "Cunningham" tables, we present tables of factorizations of a a < 100. The exponents n satisfy a if a < 30, and 100 if a 30. The factorizations are complete for n 46, and the tables contain no composite numbers smaller than 10 80 . (Update)
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76.0%: Factorizations of a^n±1, 13 ≤ a < 100 - Brent, Riele (1992) (Correct)
74.0%: Factorizations of a^n ± 1, 13 ≤ a < 100 - Brent, Riele (1992) (Correct)
24.0%: Update 1 to Factorizations of a... - Brent, Montgomery, Riele (1994) (Correct)
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0.7: Factorization of the Tenth and Eleventh Fermat Numbers - Brent (1996) (Correct)
0.5: Factorization of the Tenth Fermat Number - Brent (1999) (Correct)
0.4: How To Find Small Factors Of Integers - Bernstein (2000) (Correct)
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BibTeX entry: (Update)
@misc{ computer-factorizations,
author = "Richard Brent Computer",
title = "Factorizations of a",
url = "citeseer.ist.psu.edu/688232.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1982
134 Factoring integers with elliptic curves (context) - Lenstra - 1987
68 Prime Numbers and Computer Methods for Factorization (context) - Riesel - 1985
65 Speeding the Pollard and elliptic curve methods of factoriza.. (context) - Montgomery - 1987
51 The multiple polynomial quadratic sieve (context) - Silverman - 1987
50 The number field sieve - Lenstra, Lenstra et al. - 1990
37 Analysis and comparison of some integer factoring algorithms (context) - Pomerance - 1982
22 Some integer factorization algorithms using elliptic curves - Brent - 1986
20 Parallel implementation of the quadratic sieve (context) - Caron, Silverman - 1988
16 Factoring with the quadratic sieve on large vector computers (context) - Riele, Lioen et al. - 1989
14 Parallel algorithms for integer factorisation (context) - Brent - 1990
14 American Mathematical Society (context) - Brillhart, Lehmer et al. - 1985
12 Up to High Powers (context) - Cunningham, Woodall et al. - 1925
8 How to factor a number (context) - Guy - 1976
8 Factorization beyond the googol with MPQS on a single comput.. (context) - Riele, Lioen et al. - 1991
7 Improved techniques for lower bounds for odd perfect numbers (context) - Brent, Cohen et al. - 1991
7 Factor: an integer factorization program for the IBM PC (context) - Brent - 1989
5 Available by anonymous ftp from ftp (context) - Morain, et et al. - 1990
5 A new lower bound for odd perfect numbers (context) - Brent, Cohen - 1989
3 Factoring: algorithms, computations, and computers (context) - Buell - 1987
Documents on the same site (http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub134.html): More
Update 1 to Factorizations of a^n ± 1, 13 ≤ a <.. - Brent, Montgomery, Riele, .. (1994) (Correct)
Factorizations of a^n ± 1, 13 ≤ a < 100 - Brent, Riele (1992) (Correct)
Factorizations of a^n±1, 13 ≤ a < 100: Update 2 - Brent, Montgomery, Riele (Correct)
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