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From An excerpt from the beginning of the INTRODUCTION. SECTION I. MANNER OF USING THE TABLE. THE object of the Table is to resolve into factors any one of the million numbers lying between 4,000,000 and 5,000,000; and the Table gives directly the least factor of every number not divisible by 2, 3, or 5 between these limits. In entering the Table, the first three figures are to be found in the spaces above the headings of the columns, the next two among the headings of the columns, and the last two in the column at the left-hand side of the page. Thus to find the least factor of 4,007,293, enter the Table with 400 72 93 (on the first page of the Table) and the tabular result is 269, showing that 269 is the least factor of the number. In the case of prime numbers, a bar is printed as tabular result: thus, for example, 4,007,281 is a prime. If the given number be divisible by 2, 3, or 5, it will not be found in the Table. The least factors of such numbers may be determined by inspection if they are divisible by 2 or 5, and almost by inspection if 3 is the least factor. The first three figures of the arguments are printed in the first column of tabular results, on each page, and also whenever on the page a change occurs in these figures. To facilitate the entry of the Table, these leading figures are also printed at the outside corner of every page, in square brackets. The number printed on each page as a heading is the first of the 9000 numbers to which the page relates; these headings are not really required, as the Table is most conveniently entered by means of the leading figures in the corner; but they are retained for the sake of uniformity with the six millions of Burckhardt and Dase. The tables of Burckhardt, Dase, and Chernac, were described in Section II of the Introduction to the Fourth Million.

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