Tag: Prime Clockwork
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Elegant Addition-only Prime Generation in LISP
Brief history of LISP. LISP is a functional programming language that was created in the late 1950s by John McCarthy at MIT. It quickly became the lingua franca for symbolic AI because of its tiny, expressive core: homoiconic syntax (code-as-data), first-class functions/closures, macros that extend the language, and automatic memory management. McCarthy emphasized writing programs…
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Fundamental Theorem of Arithmetics: Zermelo’s proof in detail
The Fundamental Theorem of Arithmetic: Zermelo’s proof in detail Michael Emmerich, December 14th, 2024 Zermelo (1934) employs a proof by contradiction to establish the uniqueness of prime factorization for positive integers, demonstrating that the assumption of a non-unique prime factorization leads to a contradiction. Notably, his proof does not rely on Euclid’s Lemma. This essay…
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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…
Michael Emmerich 