Format of factor tables

I try to maintain a common format for all the factor tables stored here. The format has been designed to be easy to read by both humans and programs.

Any line which begins with a '#' character is pure commentary and should be ignored or copied unchanged as appropriate by programs. Completely blank lines should also be ignored; they shouldn't be present but this rule exists just in case they creep in by accident.

It is assumed that each file contains the factorization of only one kind of integer which is indexable by a simple numerical index (exception: Aurifeuillean factorizations of Cunningham numbers are indexed by L and M as well). The indexes need not be consecutive (for instance n^b-1 has a trivial factorization for even b, which values are therefore omitted) but they are monotonically increasing. The filename itself, possibly modified by the containing directory's name, usually specifies the type of table.

Each line contains the numerical index (indexL or indexM for Aurifeuillean factors) followed by a TAB character. The remainder of the line consists of the decimal representation of each prime factor in numerical order, separated by a '.' character. The final factor may be given either explicitly, or in the form TAB Pxyz or TAB pxyz or TABCxyz. Here, P123 represents a proven prime of 123 decimal digits, not otherwise specified, p456 represents a strong pseudoprime of 456 digits and C789 represents a composite number of 789 digits. In a few cases where algebraic or Aurifeuillean factorizations exist but are not given on separate lines, there may be more than one composite factor in the list of factors. Such factors are always given in the Cxyz form. If full decimal representation of a factor appears in the tables you can be sure that it is either a prime or strong pseudoprime.

Note that algebraic factors are not always given. Before calculating cofactors from these tables, you should always check divisibility by any algebraic factors (including repeated factors). These will, of course, be found earlier in the same table or in closely related tables.


The file "factorial-" contains the factorization of N!-1, and begins:

# Factors of n! - 1
# If you find new factors of these numbers, please let Paul Leyland
# ( and Andrew Walker ( know.
# Last update 2004 July 7
3    5
4    23
5    7.17

and ends

398    321159920984703967. C847
399    401.1709. C861
400    571521933856259. P855

Another example: some way into "cunningham/2+" we find the following factorizations of 2^n+1:

225    4714696801.281941472953710177758647201
226L    10384593717069655112945804582584321
226M    58309.2362153.15079116213901326178369
227    297371.3454631579714210387. P44

Note the Aurifeuillean factorizations and that algebraic factors are missing from the list.