| 释义 |
Legendre's FormulaCounts the number of Positive Integers less than or equal to a number  which are not divisible by any of the first  Primes,
 | (1) |
 is the Floor Function. Taking  gives | |  | | | (2) |
where  is the Prime Counting Function. Legendre's formulaholds since one more than the number of Primes in a range equals the number of Integers minus the number ofcomposites in the interval.
Legendre's formula satisfies the Recurrence Relation
 | (3) |
 , then
where  is the Totient Function, and
 | (5) |
 . If  , then
 | (6) |
Note that  is not practical for computing for large arguments. A more efficient modification isMeissel's Formula. See also Lehmer's Formula, Mapes' Method, Meissel's Formula, Prime Counting Function
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