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

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370,373 492,227 1,357,333 1,562,051 2,010,881 2,898,359 3,826,157 3,933,731 4,652,507 4,738,777 5,518,817 5,888,873 6,034,393 6,371,537 Ninth f 8,421, 18,917, 251 523 7,230,479 399 8,421,403 8,917,663 111 113 131 131 147 119 137 131 153 125 129 131 145 135 147 139 151 139 K 66 INTEODrCTlON.
[§ III.
SECTION III.
^COMPARISON OF THE RESULTS OF THE ENUMERATION WITH LEGENDRE'S, TCHEBYCHEFF'S, AND RIEMANN'S FORMULAE.
Legendre's Formula.
The fifth section of the Introduction to the Fourth Million rela
...tes to the distribution of prime numbers, and an account is there given of the diflferent formulae which have been proposed for representing approximately the number of primes inferior to a given number. The present section contains the results of comparisons between the actual numbers of primes found by the enumerations described in the preceding pages and the numbers given by these formulae.
The first formula for the approximate representation of the number of primes inferior to a given prime x was given by Legendre in the second edition (180.8) of his Essai sur la ThSorie des Nbmbres (Partly.


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