# Format of the Tables

The factor tables on this site mostly use the same format as the Cunningham tables. Details of that format can be found in the Cunningham Book, 3rd edition, section VI. The only differences are that 1) We do not split factorizations across multiple lines, and 2) The digit limit for ultimate factors to appear in the tables is 30; i.e. if the final factor on a line is 30 digits or larger in size, then it is represented by "Pxxx" or "Cxxx" if that factor is prime or composite, respectively (and "xxx" is the digit count for the factor).

For those unfamiliar with the Cunningham format, here are some salient points:

• The entry for each exponent first displays in parentheses the exponents for the algebraic factors which are part of the represented number. For details on the algebraic structure of cyclotomic numbers such as these, see the Cunningham Book, 3rd edition, section III.C.1.
• The factors shown on each line are only for the primitive part of the given number.
• Factors of the primitive part which are also factors of the algebraic part of the number are referred to as intrinsic factors. Such factors are marked with an asterisk (*) in the tables.
• Ultimate factors of at least 30 digits appear fully written out in the Primes and Composites files.

So, for example, the 3-2 table has the following entry for the exponent 203, representing the number 3203-2203:

`203 (7,29) 29*.6914587.1872620794129.P60`

The 7 and 29 in parentheses indicate that both 37-27 and 329-229 are algebraic factors of 3203-2203. The asterisk after the unparenthesized 29 indicates that it is an intrinsic factor; and indeed, a prior line in the same table tells us that 29 is also a factor of 37-27. And the P60 indicates that the largest factor of the primitive part of 3203-2203 is a prime of 60 digits, and it can be found in the Primes file. So if one wished to list out all of the prime factors of 3203-2203, one would take all of the factors found on the lines for exponents 7, 29, and 203 in the 3-2 table, as well as the P60 found in the Primes file.

Aurifeuillian factorizations require a slightly more complex format. See the Aurifeuillian page and the Cunningham Book, 3rd edition, section III.C.2 for details of their algebraic structure, and the consequent display format for their table entries.