The maxima and minima of
⟨
L
(
x
)
⟩
−
π
(
x
)
,
⟨
R
(
x
)
⟩
−
π
(
x
)
\langle L(x)\rangle - \pi (x),\langle R(x)\rangle - \pi (x)
, and
⟨
L
2
(
x
)
⟩
−
π
2
(
x
)
\langle {L_2}(x)\rangle - {\pi _2}(x)
in various intervals up to
x
=
8
×
10
10
x = 8 \times {10^{10}}
are tabulated. Here
π
(
x
)
\pi (x)
and
π
2
(
x
)
{\pi _2}(x)
are respectively the number of primes and twin primes not exceeding
x
,
L
(
x
)
x,L(x)
is the logarithmic integral,
R
(
x
)
R(x)
is Riemann’s approximation to
π
(
x
)
\pi (x)
, and
L
2
(
x
)
{L_2}(x)
is the Hardy-Littlewood approximation to
π
2
(
x
)
{\pi _2}(x)
. The computation of the sum of inverses of twin primes less than
8
×
10
10
8 \times {10^{10}}
gives a probable value
1.9021604
±
5
×
10
−
7
1.9021604 \pm 5 \times {10^{ - 7}}
for Brun’s constant.