Excerpt from Tables of the Prime Numbers, and Prime Factors of the Composite Numbers, From 1 to 100, 000: With the Methods of Their Construction, and Examples of Their Use The peculiar property of prime numbers, upon which their ordinary uses mainly depend, is that, while they themselves are incapable of being exactly measured by any ia tegral number greater than a unit, they and their products and powers do constitute all the possible measures, above a unit, of all other numbers. To render this property extensively available in the solution of problems, and especially in readily distinguishing frac tions, ratios and incommensurable roots or surds, which aie reducible, from those which are irreducible, and reducing those of them, which are reducible, to their low est terms; and in finding the least common multiple of two or more given numbers it is necessary not only that the prime numbers should be distinguished from the com posite, but that such of the prime as are measures of the composite, respectively, should be also known. And inasmuch as there is no method of determining directly Or speedily whether some of the numbers ending in 1, 3, 7 or 9, are composite or prime, or if composite, what their prime factors are; it is of great advantage, in the saving of time and labor, to have either all the factors of each of the composite num bers within convenient limits, ascertained and orderly arranged in tables, or such of them, at least, as may afford the means of readily finding the rest. Early in the year 1850, the author of this book undertook to devise some easy method for the ascertainment of prime numbers. He had not then seen any table of such numbers, nor did he know what any author had written respecting them. His ignorance on the subject was not owing so much to neglect to seek information, as to the circumstance of his not being able to obtain it from the persons or books consulted. Finding that prime numbers could not be discovered, to any great extent, by any direct method, and not assuming numbers to be prime, without demonstrating them to be so, he first devised and used, for the discovery of them, to a limited extent, the method by multiplication, as explained in Part I, Chapter II. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.