Integer Factorizations And (Cyclotomic) Polynomials

by Alfred Reich
February 9, 2010

Factorizations of numbers of shape 2009^32 + b^32

Results are listed in GF.2009.32.html (Nov 21, 2009, corrected Jan 16, 2010).
Complete. Contributors are Kurt Beschorner and Alfred Reich.

Factorizations of numbers of shape (k^2·41)^41 - 1

These numbers admit factorizations of type Aurifeuillian.
Results (up to k = 1000) are listed in Phi41z.html (Feb 5, 2010).
Please recall that the range k > 100 is not searched thoroughly.
At the moment not any newly found factor with less than 40 digits is listed in the News and Old files.
Contributors (currently) are Robert Backstrom, Kurt Beschorner, Juno Fernadez 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.html (Sep 5, 2009).
Complete. Contributors are Robert Backstrom, Kurt Beschorner and Alfred Reich.

Factorizations of numbers of shape 2009^n ± 1

Results (for n ≤ 130 and n = 138, 144, 150, 154, 159, 161, 168, 170, 208, 238, 246, 248, 270, 272 and 295) are listed in Phin2009.html (Jan 11, 2010).
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.html (Feb 8, 2010). 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

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

Related Tables and Pages

Factorizations of Repunit Numbers of the form (10ⁿ-1)/9 (Kurt Beschorner).
Factorizations of near-repdigit-related numbers (Makoto Kamada).
Factors of Repunit Numbers (Yousuke Koide).

Maintained by Alfred Reich.