Category: Mathematical Playground
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Grand Cycles of the Primes
On Periodic Patterns in the Prime Clockwork – September 15th, 2024, Michael Emmerich I have two rotating gears, with 90 and 54 teeth. When do the starting points of these gears align? — Wilson, R. (2020). Number Theory: A Very Short Introduction. Oxford University Press, Page 7 When do the gears align again? The textbook…
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Prime Clockwork
Prime Clockwork – A Simple Automaton to Generate Natural Numbers and Their Prime Factors 15.8.2024, by Michael Emmerich 1. What is the prime clockwork? This work presents the prime clockwork, an automaton that generates all natural numbers in prime factorization starting from one, using only integer addition and comparison -— no division or multiplication. The…
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Playing with Primes
A Positional Notation of Integers and Rationals Based on Prime Factorization Let denote the primes, i.e. , The fundamental theorem of number theory, as proved e.g. in (Gauss, 1870), tells us that each integer can be represented as a unique product of primes. Let us represent integers as infinite lists we call prime vectors. Definition…
Michael Emmerich 