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SUMMARY:Alexander Shen (CNRS - LIRMM\, Montpellier)
DTSTART:20231025T150000Z
DTEND:20231025T161500Z
DTSTAMP:20260423T035957Z
UID:AAIT/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AAIT/23/">In
 formation theoretic proofs (a survey).</a>\nby Alexander Shen (CNRS - LIRM
 M\, Montpellier) as part of Seminar on Algorithmic Aspects of Information 
 Theory\n\n\nAbstract\nSome theorems that have nothing to do with informati
 on theory can be proven using an information-theoretic argument (entropy\,
  or Kolmogorov complexity\, or counting via compression). For example\, wh
 y are there infinitely many prime numbers? If there were only M prime numb
 ers\, then each integer could be encoded by the list of M exponents in its
  prime decomposition\, so we could specify each n-bit number by only M×O(
 log n) bits\, a contradiction. We will discuss several examples of proofs 
 of that type\, including other bounds for the distribution of prime number
 s\, but not only them.\n
LOCATION:https://researchseminars.org/talk/AAIT/23/
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