Factor Table for the Sixth Million: Containing the Least Factor of Every Number Not Divisible by 2,3, Or 5 Between 5,000,000 and 6,000,000

Taylor & Francis, 1883 - 215 pages

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Page 6 - It will be seen from this table that the centuries with eight primes are the most numerous in the first million, the centuries with seven primes in the second and third millions, and the centuries with six primes in the fourth and fifth millions.
Page 3 - MILLION. Containing the least factor of every number not divisible by 2, 3 or 5 between 3,000,000 and 4,000,000.
Page 12 - are primes, and the numbers intermediate to the lower limit and the upper limit are all composite.
Page 16 - Tabules, which extend from 0 to 400,031. After the table Legendre remarks " II est impossible qu'une formule représente plus fidèlement une série de nombres d'une aussi grande étendue et sujette nécessairement à de fréquentes anomalies...
Page 24 - The numbers at the foot of each column give the total number of primes in the group of numbers to which the column has reference ; thus between 3,000,000 and 3,100,000 there are 6676 primes; between 3,100,000 and 3,200,000 there are 6717 primes, &c. Similar tables to the above...
Page 11 - F(x)[ - 10[fi-(10*)-log(log 1Q-')]| for -1=0.50(0.01)0, 18S, with differences of various orders. See also, parts II and III. [11] JWL Glaisher, Tables of the numerical values of the sine-integral, cosine-integral, and exponential-integral, Phil. Trans. Roy. Soc. London 150, pp.
Page 16 - D'une loi très-remarquable observée dans rémunération des nombres premiers," and commences " Quoique la suite des nombres premiers soit extrêmement irrégulière, on peut cependant trouver avec une précision très-satisfaisante, combien il ya de ces nombres depuis 1 jusqu'à une limite donnée x. La formule qui résout cette question est _ x У — log x -1-08366' log x étant un logarithme hyperbolique.
Page 19 - A = 1,08366 setzen 1,09040 1,07682 1,07582 1,07529 1,07179 1,07297 Es scheint, dass bei wachsendem n der (Durchschnitts -)Werth von A abnimmt, ob aber die Grenze beim Wachsen des n ins Unendliche l oder eine von l verschiedene Grosse sein wird, darüber wage ich keine Vermuthung.
Page 13 - GO~~v(J obtained by a method similar to that employed in the case of the dimethyl derivative, namely, by treating the product of the action of ^-nitrosodietliylaniline on diphenylcycZopentenone with hydrochloric acid.
Page 17 - ... does not seem to have been determined solely from the value a; =10,000; for, if this were the case, we should have = 1-08026, which differs from 1-08366 by 0'00340. Legendre's formula for x= 10,000 gives 1230-51. The constant does not appear to have been determined from any single value of x ; and it seems likely that it was so chosen as to represent as nearly as possible the results of the earlier enumerations. When Legendre subsequently obtained the enumeration for the numbers from 400,000...

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