1877.] 



of ike Primes in Burchhardt'' s Tables. 



49 



by Legendre, and the values found, with the same limits, by the 

 present enumeration : it will be seen that the comparatively small 

 discrepancy of 6 is due to the fact that several of the larger errors 

 compensate one another very nearly. 



In vol. ii. of Gauss's Werhe (Gottingen, 1863), pp. 436 — 443, 

 there are given in detail the results of an enumeration of the 

 primes in the first three millions: a letter from Gauss to Encke, 

 dated December 24, 1849, which is published on pp. 444 — 447 

 contains an account of the manner in which the enumeration was 

 performed. It was commenced by Gauss as early as 1792 or 1793, 

 when he first obtained a copy of Lambert's Supplementa, which 

 contains a list of primes up to 102,000. Subsequently when 

 Vega's Tabulm of 1796^ appeared he was able to extend the 

 enumeration to 400,031. 



In 1811 Chernac's Gribrum Arithmeticuni was published, to 

 the great joy of Gauss, who states that, although he had not 



1 I have seen two copies of Vega's Tabula, and tliey both bear the date 1797. 

 Probably Gauss was writing from memory; but it is possible that some copies of 

 the Tabulce may have been circulated at the end of 1796. The preface is dated 

 February 1, 1797. 



