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