Meissel's Formula
A modification of Legendre's Formula for the Prime Counting Function 
. It starts with
 |  |  | |
 |  | (1) |
where
is the Floor Function, 
is the number of Integers 
with
, and 
is the number of Integers 
with 
.Identities satisfied by the 
s include | (2) |
and | |  | |
|  | (3) |
Meissel's formula is
 | |  | |
|  | (4) |
where
 |  |  | (5) |
 | |  | (6) |
Taking the derivation one step further yields Lehmer's Formula.See also Legendre's Formula, Lehmer's Formula, Prime Counting Function
References
Riesel, H. ``Meissel's Formula.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, p. 12, 1994.
- Angle Bracket
- Angle of Parallelism
- Angle Trisection
- Angular Acceleration
- Angular Defect
- Angular Distance
- Angular Velocity
- Anharmonic Ratio
- Anisohedral Tiling
- Annihilator
- Annulus
- Annulus Conjecture
- Annulus Theorem
- Anomalous Cancellation
- Anomalous Number
- Anonymous
- Anosov Automorphism
- Anosov Diffeomorphism
- Anosov Flow
- Anosov Map
- ANOVA
- Anthropomorphic Polygon
- Anthyphairetic Ratio
- Antiautomorphism
- Anticevian Triangle