2900 



Distribution of Prime Numbers 



2900 



Number of primes below given limit, Legendre's 



formula. Glaisher, J. W. L. [1879] Camb. 



Ph. S. P. 3 (1880) 296-. 



, Eiemann's formula, applica- 

 tion. Mangoldt, H. von. Crelle J. Mth. 



119 (1898) 65-. 

 100,000,000. Meissel, E. Mth. A. 



3 (1871) 523-; 21 (1883) 304. 

 1,000,000,000. Meissel, E. Mth. 



A. 25 (1885) 251-. 



n. Lugli, A. G. Mt. 26 (1888) 86-. 



, determination when number 



under \/n is known. Graefe, F. Z. Mth. 



Ps. 39 (1894) 38-. 



, theorem of Legendre's. Syl- 

 vester, J. J. C. B. 96 (1883) 463-. 

 between given limits. Drach, S. M. 



Ph. Mg. 24 (1844) 192-. 

 . Meissel, E. [1869] Mth. A. 



2 (1870) 636-. 

 . Oppermann, L. Kjtfb. Ov. 



(1882) 169- ; (Resume, 9-). 

 . Voile, G. Em. N. Line. 



Mm. 14 (1898) 143-. 

 , analytical expression for. 



Levi-Civita, T. Em. E. Ac. Line. Ed. 4 



(1895) (Sem. 1) 303-. 

 . , Tchebycheff 's theory. Syl- 



vester, J. J. Am. J. Mth. 4 (1881) 230-. 

 , theorem of Sylvester's. 



Gegenbauer, L. Mh. Mth. Ps. 10 (1899) 370-. 

 100,000,001 and 100,001,699. 



Davis, W. Liouv. J. Mth. 11 (1866) 188-. 

 and 2N, formulae for. Piarron 



de Hondesir, E. S. As. Fr. C. E. (1877) 79-. 

 7i + l and 2n, etc. Catalan, E. C. 



[1882] Liege S. Sc. Mm. 10 (1883) (No. 1), 



12 pp. 

 . x and (1 + h) x, theorem of Stieltjes. 



Cahen, . C. E. 116 (1893) 490. 

 Numbers prime to and less than product of 



first 7i primes, properties. Walla, F. Arch. 



Mth. Ps. 66 (1881) 353-. 

 Prime-pairs, enumeration. Glaisher, J. W. L. 



[1878] B. A. Ep. (1878) 470- ; Mess. Mth. 



8 (1879) 28-. 

 Primes in Burckhardt's and Dase's tables, 



enumeration. Glaisher, J. W. L. [1876-77] 



Camb. Ph. S. P. 3 (1880) 17-, 47-; B. A. 



Ep. (1877) (Sect.) 20-. 

 , construction of a table. Laisant, C. A, 



As. Fr. C. E. (1891) (Ft. 2) 165-. 

 , criteria. Montferrier, A. S. de. Quetelet 



Cor. Mth. 5 (1829) 94-. 



, . Warner, J. D. Am. As. P. (1890) 54-. 

 , , and factors. Seelhoff, P. Am. J. Mth. 



8 (1886) 39-. 

 , distribution problems. Pandau, E. Par. 



S. Mth. Bll. 28 (1900) 25-. 



of form 4w + l and 4n + 3, distribution. 

 Tcheblcheff, P. St Pet. Ac. Sc. Bll. 11 

 (1853) 208. 



, separate enumeration. 

 Glaisher, J. W. L. B. A. Ep. (1878) 470- ; 

 E. S. P. 29 (1879) 192-. 



100n + 1, enumeration. Daublebsky 



von Sterneck, E. Wien Az. 31 (1894) 2-. 



Primes of forms 4s + 1, 4s -1, theorems. Ge- 



geubauer, L. Mh. Mth. Ps. 4 (1893) 89-, 



98, 184. 

 , formulae, general. Polignac, A. (Prince de). 



Toul. Mm. Ac. 1 (1857) 308-. 

 , properties and distribution. Polignac, A. 



(Prince de). C. E. 29 (1849) 397, 738-. 



in relation to an arithmetical progression. 

 Polignac, A. (Prince de). C. E. 54 (1862) 

 158. 



, report on calculations made by Bertelsen. 



Gram, J. P. Acta Mth. 17 (1893) 301-. 

 , theorem. Laurent, H. C. E. 126 (1898) 



809-. 

 Eecurring series, application. Lucas, E. C. 



E. 82 (1876) 165- ; 83 (1876) 1286-. 

 Eiemann's function, maximum value. Preo- 



braiemkij, P. V. Mosc. S. Sc. Bll. 78 



(No. 1) (1892) 27-; Fschr. Mth. (1892) 170. 



f(), Bourget,. C. E. 101 (1885) 304- . 



. Jensen, J. L. W. V. C. E. 104 



(1887) 1156-. 



. Gram, J. P. Kjtfb. Ov. (1895) 303-. 



. Landau, E. C. E. 129 (1899) 812-. 



, and analogous functions. Cahen, E. 



Par. EC. Norm. A. 11 (1894) 75-. 

 , number of primes below given 



limit. La Vallee-Poussin, C. J. de. Brux. 



Mm. Cour. 8, 59 (1899-1900) No. 1, 74 pp. 



for a odd and positive, values. 

 Kluyver, . Bll. Sc. Mth. 20 (1896) 116-. 



, zeros. Hadamard, . C. E. 122 



(1896) 1470-; 123 (1896) 93; Par. S. Mth. 



Bll. 24 (1896) 199-. 

 f(x) and logarithmic integral. Phrag- 



m4n, E. Stockh. Ofv. (1891) 599-. 

 (t), arithmetical application. Franel, J. 



Zur. Vjschr. 41 (1896) (Festschr., Th. 2) 7-. 

 f, property. Mertens, F. Wien Ak. Sb. 



107 (1898) (Ab. 2a) 1429-. 



prime number formula, calculation of some 

 terms. Phragmen, E. Stockh. Ofv. (1891) 

 721-. 



Series of primes. Smith, H. J. S. Ashmol. 



S. P. 35 (1857) 128-. 

 . Lorenz, L. V. (xn) Ts. Mth. 2 



(1378) 1-. 

 Sieve of Eratosthenes. Colombier, P. A. G. 



N. A. Mth. 2 (1843) 408-. 



, extension. Bunlakovskij , V. Ja. 

 St Pet. Ac. Sc. Mm. (Rs.) 41 (*1882) 

 (Suppl.) No. 3, 32 pp. 



, historical notice. Polignac, A. 

 (Prince de). N. A. Mth. 12 (1853) 429-. 



, six arithmological propositions de- 

 duced from. Polignac, A. (Prince de). N. 

 A. Mth. 8 (1849) 423-. 



for primes. Speckmann, G. Arch. Mth. Ps. 

 11 (1892) 439-; 12 (1894) 431-. 



. Schapira, H. [1896] D. Mth. Vr. 



Jbr. 5 (1901) (Heft 1) 69-. 



. Christie, R. W. D. Nt. 56 (1897) 10-. 



; number of primes; series of odd 



numbers. Terquem, O. N. A. Mth. 5 (1846) 



607-. 

 Sum of logarithms of primes not exceeding x. 



Cahen . C. E. 116 (1893) 86-. 



227 



p2 



