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math.GM2021
All the information in the integers is in the primes
Aidan Rocke
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} \c…
math.GM2021
An information-theoretic upper bound on prime gaps
Aidan Rocke
Within the setting of rare event modelling, the method of level sets allows us to define an equivalence relation over rare events with distinct rates of entropy production. This me…