PEOCEEDINGS 



OF THE 



February 11, 1878. 

 Professor Liveing, President, in the chair. 



The following comnrnnication was made to the Society : — 



Mr J. W. L. Glatsher, M.A., F.R.S., On factor tables, with an 

 account of the mode of formation of the factor table for the fourth 

 onillion^. 



§ 1. If it be required to determine whether a given number 

 is prime or not, the only available method (in the absence of 

 tables) is to divide it by every prime less than its square root, or 

 until one is found that divides it Avithout remainder^ If, on the 

 other hand, the object is to form a table of prime numbers, the 

 process is theoretically very simple and rapid. For, suppose all 

 the natural numbers ranged in order in one straight line at equal 

 distances, thus : 



1— li-Hr^rHT— It— It— Ir— li— li— iCNCN*** 



1 This paper has been considerably amplified since it was read to the Society. 

 J. W. L. G. (June, 1878). A table of contents is given at the end of the paper 

 (p. 137). 



2 Euler commences his memoir " Quomodo numeri prsemagni sint explorandi, 

 utrum sint primi, nee ne" (Opera minora coUecta, St Petersburg, 1849, t. i. 

 pp. 379 — 390) as follows: "Ante omnia monendum est, me hie non ejusmodi 

 methodum polliceri, cujus ope omnes omnino numeri, cujuscunque sint generis, 

 examinari queant, utrum sint primi, nee ne? Hujusmodi enim methoduni yix 

 aliam dari posse existimo, nisi quae ad regulam redeat vulgarem, qua divisio 

 per omnes numeros primos, radice quadrata numeri propositi minores, est ten- 

 tanda, quse operatio sane, si numeri saltem medioeriter magni proponantur, 

 nimis est molesta, quam ut suscipi queat." Euler's method relates only to primes 

 of the form in + 1 which as is well known are expressible as the sum of two 

 squares in one, and only one, way. 



Vol. III. Pt. iv. ^ 



