1876.] Frof. Hughes., On the evidence for Pre-glacial Man. 17 



dence to prove that the beds in which the flint implements 

 occurred belonged to the valley gravels and brickearths of the 

 same age as those from which they have long been known. By 

 reference to sections he showed that there were at least three 

 different horizons at which similar loams occurred in that district, 

 omitting the most recent subaerial deposits, and that it was owing 

 to a wrong ideutification of these loams that the mistake had 

 arisen. 



December 4, 1876. 

 Prof. Clerk Maxwell, r.R.S., President, in the Chair. 



The following communications were made to the Society : 



(1) Mr J. W. L. Glaisher, M.A., F.R.S. : Preliminary account 

 of the results of an enumeration of the primes in Base's tables 

 (6,000,000 to 9,000,000). 



The existing factor tables are : Chernac's Cribrum Arithme- 

 ticum (1811), giving all the divisors of every number up to 

 1,020,000 ; Burckhardt's Tables des diviseurs (1814—1817), giving 

 the least divisor of every number up to 3,036,000 ; and Dase's 

 Factoren Tafeln (1862 — 1865), giving the least divisor of every* 

 number from 6,000,000 to 9.,OOO,O0O. There is thus left a gap of 

 three millions for which there are no printed tables ; the tables 

 exist in manuscript at Berlin, but hav« not been published. 



In 1871 I commenced the enumeration of the primes in the 

 six millions over which the published tables extend. The work 

 was performed in duplicate by two computers, quite independently: 

 the two enumerations were then read with one another and the 

 discrepancies marked. All the doubtful numbers in both were 

 then examined independently, and the two pieces of work were 

 brought into agreement. Subsequently one of them was ex- 

 amined de novo throughout with the original tables. 



A short account of the enumeration, as far as it had then 

 proceeded, together with an abstract of the results for two of the 

 millions, was published in the Report of the British Association, 

 for 1872^ I have there given tables showing the agreement of 

 the numbers of primes counted with the theoretical numbers 

 derived from the logarithm-integral formula of Tchebycheff and 

 Hargreave, for the second and ninth millions, arranged in groups 



1 Multiples of 2, 3 or 5 are excluded from Chernac's, Burekliardt's and Dase's 

 tables, as for such numbers the least factor is determined either at sight or almost 

 at sight. 



^ ' Ou the law of distribution of prime numbers.' Transactions of the Sections, 

 pp. 19—21. 



Vol. III. Pt. i. 2 



