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
Maintained by Alfred Reich.