The Cunningham Project is a collaborative effort started in 1925 to factor numbers of the form bn ± 1 for b = 2, 3, 5, 6, 7, 10, 11, 12 and large n. The project is named after Allan Joseph Champneys Cunningham, who published the first version of the table together with Herbert J.
bm + 1 is a factor of bn − 1, if m divides n and the quotient is odd.
The following equations give aurifeuillean factors for the Cunningham project bases as a product of F, L and M:[4] Let b = s2 × k with squarefree k, if one of the conditions holds, then
Any factor of a Fermat number 22n + 1 is of the form k2n+2 + 1. bn − 1 is denoted as b,n−.
When dealing with numbers of the form required for aurifeuillean factorization, b,nL and b,nM are used to denote L and M in the products above.
[5] References to b,n− and b,n+ are to the number with all algebraic and aurifeuillean factors removed.