The work opens with a terse header stating it contains factorials from 1! to 10000!, sampled at three different intervals: every integer from 1! to 99!, every hundred from 100! to 900!, and every thousand from 1000! to 10000!. The program used to compute these values, described as a simple Scheme program, has had its source code lost. This immediately frames the text as a computational artifact rather than a traditional mathematical exposition.

Each factorial is presented as a single line of digits, followed by a parenthetical note indicating the end of that entry and its digit count. For example, 1! is shown as "1" with "(end 1! — 1 digit)". This consistent formatting allows the reader to quickly verify the magnitude of each factorial and observe the rapid growth in digit length.

Format and Interval Structure

The listing is organized into three distinct blocks, each introduced by a comment line: ** 1! to 99! by 1's, ** 100! to 900! by 100's, and ** 1000! to 10000! by 1000's. The first block provides a dense sequence of consecutive factorials, allowing the reader to trace the incremental multiplication. The second block jumps by hundreds, offering snapshots of factorial growth at larger intervals. The final block samples only the thousand marks, where the numbers become extremely large—10000! spans over 35,000 digits.

This structure suggests the work was designed for reference rather than continuous reading. The intervals were likely chosen to balance comprehensiveness with file size, as the full set of every factorial up to 10000 would be impractically large. The digit counts appended to each entry serve as a quick measure of magnitude, and the trailing zeros become increasingly prominent in later entries.

Digit Counts and Trailing Zeros

Each factorial entry is followed by a parenthetical note stating the number of digits. For instance, 1! has 1 digit, 10! has 7 digits, and 100! has 158 digits. These counts grow roughly linearly with the factorial index, but the rate of increase slows logarithmically. The digit counts themselves form a sequence that could be used to approximate the logarithm of the factorial.

Trailing zeros are also evident in the formatting: the digits are often grouped in blocks of five, and the final groups may consist entirely of zeros. For example, 7000! ends with a long string of zeros, and the entry for 8000! similarly shows many trailing zeros. These zeros arise from factors of 10 in the multiplication, and their count can be computed from the exponent of 5 in the factorial. The text does not explicitly count trailing zeros, but the visual pattern is unmistakable.

Computational Origin and Lost Source Code

The header notes that the factorials were calculated using a simple Scheme program, the source code of which has been lost. This detail gives the work a particular historical character: it is a product of early digital computing and open-source distribution, preserved in its output form even though the generating program is no longer available. The choice of Scheme, a dialect of Lisp, reflects the academic and research contexts where such languages were used for symbolic computation.

The loss of the source code means that the exact algorithm used—whether it employed arbitrary-precision arithmetic, caching, or other optimizations—is unknown. However, the output itself is self-contained and can be verified independently. The work thus stands as a numerical record whose provenance is partially obscured, inviting readers to treat it as a primary data source rather than a derived table.

Reading the Work as a Reference

This is not a book to be read linearly from start to finish. Instead, it functions as a lookup table for specific factorial values or for studying patterns in digit length and trailing zeros. A reader interested in a particular factorial, say 50!, can locate it in the first block (since 50 is between 1 and 99). For factorials like 500!, one must consult the second block (100! to 900! by 100's). For 5000!, the third block provides the value.

The digit counts appended to each entry allow quick estimation of magnitude without scanning the full number. The work also enables comparisons: for instance, one can observe that 100! has 158 digits while 200! has 375 digits, illustrating the super-exponential growth. The trailing zeros become more numerous at higher factorials, and the blocks of zeros in the later entries are visually striking. The work is best used as a companion to computational or mathematical exploration.

The work's value lies in its raw numerical data, presented without interpretation or commentary. Readers should approach it as a reference tool: to look up a specific factorial, to study the growth of digit counts, or to verify computations. The lost source code and the simple formatting remind us that this is a product of early digital scholarship, preserved for its utility. For those interested in the mathematics of factorials, this list provides concrete examples that can be used to test formulas or to appreciate the sheer size of these numbers.