Lehmer's formula is a formula for the prime counting function,
 |  | ![|_x_|-sum_(i=1)^(a)|_x/(p_i)_|+sum_(1<=i<=j<=a)|_x/(p_ip_j)_|-...+1/2(b+a-2)(b-a+1)-sum_(a<i<=b)pi(x/(p_i))-sum_(i=a+1)^(c)sum_(j=i)^(b_i)[pi(x/(p_ip_j))-(j-1)],](/images/equations/LehmersFormula/Inline3.svg) |
(1)
|
where 
is the floor function,
 |  |  |
(2)
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 |  |  |
(3)
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 |  |  |
(4)
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 |  |  |
(5)
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and 
is the prime counting function. It is related
to Meissel's formula.
Lehmer's Formula
See also
Meissel's Formula, Prime Counting FunctionExplore with Wolfram|Alpha
References
Riesel, H. "Lehmer's Formula." Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 13-14, 1994.Referenced on Wolfram|Alpha
Lehmer's FormulaCite this as:
Weisstein, Eric W. "Lehmer's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LehmersFormula.html