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.

Examples:

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

# (paul@leyland.vispa.com) and Andrew Walker (ajw01@uow.edu.au) 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.