factorization_of_integers_of_special_forms

a^n \pm 1 for a = 2, 3, 5, 6, 7, 10, 11, 12 and large exponents n [http://homes.cerias.purdue.edu/~ssw/cun/index.html]
a^n \pm 1 for a ≤ 13 and a not a perfect number [http://wwwmaths.anu.edu.au/~brent/factors.html]
2^n \pm 1 for 1200 < n < 10000 [http://www.euronet.nl/users/bota/medium-p.htm]
10^n \pm 1 for n ≤ 100 [http://www.swox.com/gmp/repunit.html]
p^p \pm 1 where p is a prime number and p < 180. [http://homes.cerias.purdue.edu/~ssw/bell]
2^{2^n} + 1 (Fermat numbers) [http://www.prothsearch.net/fermat.html]
2^{3^n} \pm 1 [http://www.alpertron.com.ar/MODFERM.HTM]
Fibonacci numbers (F_n) and Lucas numbers (L_n) for n < 10000 [http://home.att.net/~blair.kelly/mathematics/fibonacci/]
n*2^n \pm 1 (Cullen and Woodall numbers) [http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm]
Euclid numbers [http://en.wikipedia.org/wiki/Sylvester's_sequence#Divisibility_and_factorizations]