Chap. XIII] FaCTOK TaBLES, LiSTS OF PRIMES. 355 
A. Cunningham^^ noted errata in various factor tables. 
*J. R. Akerlund^^" discussed the determination of primes by a machine. 
Gaston Tarry^^ would use an auxiliary table (as did Barlow in 1819) 
to tell by the addition of two entries (< |p) if a given number < iV is divisible 
by a chosen prime p. For N = 10000, he used the base 6 = 100, and gave a 
table showing the numerically least residues of the numbers r<h and the 
multiples of b for each prime p<b. Then nh-\-r is divisible by p if the 
residues of nh and r are equal and of opposite sign. For A^ = 100 000, he 
used 6 = 60060 = 2-91-330 and wrote numbers in the form m6+330g+r, 
q<90, r<330; or, again, 6 = 20580. Ernest Lebon" used such tables with 
the base 30030 = 2-3-5-7-lM3, or its product by 17. 
Ernest Lebon,^^ J. Deschamps,^^ and C. A. Laisant^'''' discussed the con- 
struction of factor tables. 
J. C. Morehead^° extended the sieve of Eratosthenes to numbers 
ma^+6 (m = l, 2, 3,. . .) in any arithmetical progression. The case a = 2, 
6= ±1, is discussed in detail, with remarks on the construction of a table 
to serve as a factor table for numbers m-2''=t 1. 
L. L. Dines^^ treated the case a = 6, 6 = =fcl, and the factorization of 
numbers m-Q'^^l. 
D. N. Lehmer^^ gave a factor table to 10 million and listed the errata in 
the tables by Burckhardt, Glaisher, Dase, Dase and Rosenberg, and 
Kulik's tenth million, and gave references to other (shorter) lists of errata. 
E. B. Escott^^" listed 94 pairs of consecutive large numbers all of whose 
prime factors are small. 
L. Aubry^^° proved that a group of 30 consecutive odd numbers does not 
contain more than 15 primes or numbers all of whose prime factors exceed 7. 
Cunningham^^" listed the numbers of 5 digits with prime factors ^ 11 . 
85Messenger Math., 34, 1904-5, 24-31; 35, 1905-6, 24. 
ss^Nyt Tidsskrift for Mat., Kjobenhavn, 16A, 1905, 97-103. 
8«Bull. Soc. Philomathique de Paris, (9), 8, 1906, 174-6, 194-6; 9, 1907, 56-9. Sphinx-Oedipe, 
Nancy, 1906-7, 39-41. Tablettes des Cotes, Gauthier-Villars, Paris, 1906. Assoc, 
frang. avanc. sc, 36, 1907, II, 32-42; 41, 1912, 38-43. 
"Comptes Rendus Paris, 151, 1905, 78. Bull. Amer. Math. Soc, 13, 1906-7, 74. L'enseignement 
math., 9, 1907, 185. Bull. Soc. PhUomathique de Paris, (9), 8, 1906, 168, 270; (9), 10, 
1908, 4-9, 66-83; (10), 2, 1910, 171-7. Assoc, frang. avanc. sc, 36, 1907, II, 11-20, 
49-55; 37, 1909, 33-6; 41, 1912, 44-53; 43, 1914, 29-35. Rend. Accad. Lincei, Rome, (5), 
15, 1906, I, 439; 26, 1917, I, 401-5. Sphinx-Oedipe, 1908-9, 81, 97. BuU. Sc. Math. 
El6m., 12, 1907, 292-3. II Pitagora, Palermo, 13, 1906-7, 81-91 (table serving to factor 
numbers from 30030 to 510 510). Table de caract6ristiques relatives a le base 2310 des 
facteurs premiers d'un nombre inf^rieur k 30030, Paris, 1906, 32 pp. Comptes Rendus 
Paris, 159, 1914, 597-9; 160, 1915, 758-760; 162, 1916, 346-8; 163, 1916,259-261; 164, 
1917, 482-4. 
*8Jomal de sciencias math., phys. e nat., acad. sc. Lisbona, (2), 7, 1906, 209-218. 
89Bull. Soc. Philomathique de Paris, (9), 9, 1907, 112-128; 10, 1908, 10-41. 
s'^Assoc. frang., 41, 1912, 32-7. 
soAnnals of Math., (2), 10, 1908-9, 88-104. ^Ubid., pp. 105-115. 
s^Factor table for the first ten milhons, Carnegie Inst. Wash. Pub. No. 105, 1909. 
'^''Quar. Jour. Math., 41, 1910, 160-7; I'interm^diaire des math., 11, 1904, 65; Math. Quest, 
Educ. Times, (2), 7, 1905, 81-5. 
"bSphinx-Oedipe, 6, 1911, 187-8; Problem of Lionnet, Nouv. Ann. Math., (3), 2, 1883, 310. 
'^'^Math. Quest. Educ. Times, (2), 21, 1912, 82-3. 
