Chap. XIII] FACTOR TABLES, LiSTS OF PRIMES. 353 
J. W. L. Glaisher" gave for the second and ninth millions the number of 
primes in each interval of 50000 and a comparison with lix' — lix, where 
lix = jdx/log X [more precise definition at the end of Ch. XVIII]. 
A committee^^ consisting of Cayley, Stokes, Thompson, Smith, and 
Glaisher prepared the Report on Mathematical Tables, which includes 
(pp. 34-9) a list of factor and prime tables. 
J. W. L. Glaisher^^ described in detail the method used by his father^" 
and gave an account of the history of factor tables. 
Glaisher^^" enumerated the primes in the tables of Burckhardt and Dase. 
Glaisher^^^ tabulated long sets of consecutive composite numbers. He^^" 
enumerated the prime pairs (as 11, 13) in each successive thousand to 3 
million and in the seventh, eighth, and ninth millions. 
E. Lucas^^'' wrote P(q) for the product of all the primes ^ q, where q 
is the largest prime < n. If xP(g)±l are both composite, xP{q)—n,. . ., 
xP{q),. . ., xP{q)-\-n give 2n+l composite numbers. 
Glaisher^^' enumerated the primes 4n4-l and the primes 4n+3 for inter- 
vals of 10000 in the kth milUon for k = l,2, 3, 7, 8, 9. 
James Glaisher'^° filled the gap between the tables by Burckhardt^^ and 
Dase". The introduction to the table for the fourth million gives a history 
of factor tables and their construction. Lehmer^^ praised the accuracy of 
Glaisher's table, finding in the sixth million a single error besides two mis- 
prints. 
Tuxen'^^ gave a process to construct tables of primes. 
Groscurth and Gudila-Godlewksi, Moscow, 1881, gave factor tables. 
*V. Bouniakowsky'^^" gave an extension of the sieve of Eratosthenes. 
W. W. Johnson'^^'' repeated Glaisher's'^° remarks on the history of tables. 
P. Seelhoff^^ gave large primes /c-2"+l {k< 100) and composite cases. 
Simony'^^ gave the digits to base 2 of primes to 2^^ = 16384. 
L. Saint-Loup^^ gave a graphical exposition of Eratosthenes' sieve. 
H. Vollprecht'^^ discussed the construction of factor tables. 
"Report British Association for 1872, 1873, trans., 19-21. Cf. W. W. Johnson, Des Moines 
Analyst, 2, 1875, 9-11. 
68Report British Association for 1873, 1874, pp. 1-175. Continued in 1875, 305-336; French 
transl., Sphinx-Oedipe, 8, 1913, 50-60, 72-79; 9, 1914, 8-14. 
"Proc. Cambridge Phil. Soc, 3, 1878, 99-138, 228-9. 
69'»/6id., 17-23, 47-56; Report British Assoc, 1877, 20 (sect.). Extracts by W. W. Johnson, 
Des Moines Analyst, 5, 1878, 7. 
s'^-Messenger Math., 7, 1877-8, 102-6, 171-6; French transl., Sphinx-Oedipe, 7, 1912, 161-8. 
^^'^Ibid., 8, 1879, 28-33. 
«9«*/6id., p. 81. C. Gill, Ladies' Diary, 1825, 36-7, had noted that xP(q)+j is composite for 
j = 2,...,q-l. 
BseReport British Assoc, 1878, 470-1; Proc. Roy. Soc. London, 29, 1879, 192-7. 
^"Factor tables for the fourth, fifth and sixth millions, London, 1879, 1880, 1883. 
"Tidsskrift for Mat., (4), 5, 1881, 16-25. 
'i«Memoirs Imperial Acad. Science, St. Petersburg, 41, 1882, Suppl, No. 3, 32 pp. 
"^Annals of Math., 1, 1884-5, 15-23. 
"Zeitschrift Math. Phys., 31, 1886, 380. Reprinted, Sphinx-Oedipe, 4, 1909, 95-6. 
"Sitzungsber. Ak. Wiss. Wien (Math.), 96, II, 1887, 191-286. 
^^Comptes Rendus Paris, 107, 1888, 24; Ann. de I'^cole norm., (3), 7, 1890, 89-100. 
"Ueber die Herstellung von Faktorentafehi, Diss. Leipzig, 1891. 
