i22 Mr Glaisher, On factor tables. [Feb. 11, 



who was at Lisbon, and had issued a Latin announcement of his 

 factor table to 24,600,000. 



This is the last mention I have found of Felkel. It will be 

 seen that ' Opfer der Zernichtung ' was not too strong a description 

 of the fate of the table. Felkel seems to have continued to issue 

 factor table circulars to the last. 



Thus of all the persons — Oberreit, von Stamford, Rosenthal, 

 Felkel, Hindenburg — who were induced to calculate large factor 

 tables by Lambert's promise of immortality, Felkel is the only 

 one who has left any record of his work : and that consists only 

 of a very curious and rare book, of which the Graves copy is 

 perhaps almost the only one that extends as far as to 408,000. 



§ 12. The fact that so many calculations should have been 

 commenced and none completed, is due partly to the peculiar 

 character of the work, which requires continual and persistent 

 attention throughout, and is of such a kind that it does not permit 

 of being laid aside and resumed after an interval, and partly 

 to the difficulty of arranging the table in a compact form if all the 

 factors are to be given. Both Felkel and Hindenburg employed 

 large folio pages. 



Lambert attached great importance to the table giving all the 

 factors ; and this seems to me to have been unfortunate, as the 

 bulk of the book is thereby greatly increased. I have in § 1 

 expressed a strong opinion that all that is wanted is the power to 

 readily resolve a number into factors, and this is obtained if the 

 least factor is given. It is undoubtedly more convenient to have 

 all the prime factors : but to give all the factors is a luxury, as 

 distinguished from a necessity. Up to 10,000 or 100,000 I should 

 consider it most desirable to have a table, giving all the prime factors 

 with their powers, for ready reference in cases in which it might 

 be necessary to find a number having factors of a given form, or 

 having a certain number of factors, &c.; but the primary object of 

 a factor table is to save the labour of dividing a number by all the 

 primes 7, 11, 13, 17... in order to find whether it is prime, or what 

 are its factors. As a matter of fact, Chernac's table gives all 

 prime factors up to a million, and it is very convenient to have the 

 complete resolutions of numbers to this extent ; but ex. gr. I should 

 regard a table giving the least factors for a range of two millions 

 as more valuable than a table giving the complete resolutions for 

 one million. 



§ 13. From the list in § 3 it will be seen that Marci published 

 a list of primes to 400,000 in 1772. Neither Lambert nor any of 

 his correspondents knew anything of this table, nor does Gauss 

 refer to it. I have not seen it, and all that I know of it is 



