  Building upon the work of Chebyshev, Shannon and Kontoyiannis, it may be
demonstrated that Chebyshev's asymptotic result: \begin{equation} \ln N \sim
\sum_{p \leq N} \frac{1}{p} \cdot \ln p \end{equation} has a natural
information-theoretic interpretation as the information-content of a typical
integer $Z \sim U([1,N])$, sampled under the maximum entropy distribution, is
asymptotically equivalent to the information content of all primes $p \leq N$
weighted by their typical frequency. This result is established by showing that
the correct information-theoretic interpretation of the entropy $\ln p$ may be
deduced from the author's recent observation that the prime numbers have a
uniform source distribution. Moreover, using Chaitin's theorem that almost all
integers are algorithmically random we may extend this asymptotic result to the
setting of algorithmic information theory and derive an upper-bound on the
algorithmic information of a typical integer.
