Integer Factorizations And (Cyclotomic) Polynomials

by Alfred Reich

May 18, 2012

Factorizations of numbers of shape a^(2^m) + b^(2^m)

a m file information
13 7 GF.13.7.txt Mar 29, 2011 (complete)
14 7 GF.14.7.txt Oct 27, 2011 (complete) (with contributions by Mathew)
15 7 GF.15.7.txt Dec 27, 2011 (complete)
16 7 GF.16.7.txt Dec 27, 2011 (complete)
17 7 GF.17.7.txt Jan 2, 2012 (complete) (with contributions by Mathew)
18 7 GF.18.7.txt Jul 27, 2011 (complete) (with contributions by Mathew)
20 7 GF.20.7.txt Jan 27, 2012 (complete)
41 6 GF.41.6.txt Jan 6, 2011 (complete)
41 7 GF.41.7.txt Feb 6, 2012 (14 composites) (with contributions by Kurt Beschorner)
41 8 GF.41.8.txt Apr 4, 2011 (30 composites)
41 9 GF.41.9.txt Mar 21, 2011 (36 composites)
41 10 GF.41.10.txt Nov 11, 2011 (37 composites) (with contributions by Kurt Beschorner)
49 6 GF.49.6.txt Feb 7, 2011 (complete)
2009 5 GF.2009.5.txt Nov 21, 2009 (complete) (with contributions by Kurt Beschorner)
2010 5 GF.2010.5.txt Jan 1, 2011 (complete)
2011 6 GF.2011.6.txt Apr 30, 2012 (1372 composites) (with contributions by Kurt Beschorner and Norbert Schneider)
2012 5 GF.2012.5.txt Jan 1, 2012 (complete)

Contributions are welcome.
Any factor, any size.

Factorizations of numbers of shape z^41 − 1 with 1000 < z

Results are written to the files Phi41z.txt (May 18, 2012) and Phi41z.UpTo2000.txt (Feb 6, 2012).
Contributors (currently) are Robert Backstrom, Kurt Beschorner, Juno Fernadez, Mathew, Oscar Östlin and Alfred Reich.
Contributions are welcome.

Factorizations of numbers of shape 100^n + 3 · 10^n + 43 with n ≤ 100

Let P(X) := X^2 + X + 41 (Euler's polynomial).
Substituting X := 10^n + 1, we get the series 100^n + 3 · 10^n + 43.
Factorization results are listed in EulerTenPlus.txt (Sep 5, 2009).
Complete.
Contributors are Robert Backstrom, Kurt Beschorner and Alfred Reich.

Factorizations of numbers of shape 2009^n − 1 with n ≤ 300

Results are listed in Phin2009.txt (Jan 23, 2012).
Contributors (currently) are Robert Backstrom, Kurt Beschorner, Kenji Ibusuki and Alfred Reich.
Contributions are welcome.

Factorizations of numbers of shape 10^n + 1 with n ≤ 12000

In the past, this site collected factors of numbers of shape 10^n + 1 (with n up to 12000). Kurt Beschorner and Alban Nonymous contributed a lot of new factors. The result of our efforts is summarized in TenPlus.txt (May 18, 2012). Additionally, this file contains annotations on the name of the finder of some factors (at the best of my knowledge).
If you are interested in numbers with larger exponents or in numbers of shape 10^n − 1, you should look at Makoto Kamada's very frequently updated list Phin10.txt.

New and Old

2012: May April March February January
2011: December November October September August July June May April March February January
2010: December November October September August July June May April March February January
2009: December November October September August July June May April March February January 
2008: December

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