![]() The patterns in question are revealed in hybrid period-24 digital root ↔ modulo 90 congruence matrices found in our section devoted to Factorization and in a paper by the undersigned titled "From Vedic Square to the Digital Root Clockworks of Modulo 90 Factorization" published in the September, 2018 edition of the online International Journal of Vedic Mathematics (Note: link opens. This methodology combining congruence relations with digital root cycles exposes palindromes and complex polygons that illuminate our understanding of how prime numbers are formed. One might call what follows 'primal math' in that its modular arithmetic is revealed to be deeply rooted in the most deceptively primitive mathematics of all–digit sum and digital root arithmetic (and especially the Vedic Square that originated in ancient India). We will also demonstrate how the Prime Spiral Sieve can geometrically shapeshift into a rectangular matrix, 4-sided pyramid, or continuous triangular wave.Īnd we will show how the first three primes, 2, 3, and 5–although excluded from our factorization domain by definition–are nonetheless omnipresent in the form of structure serving to contain and direct the aforementioned factorization algorithms. These deterministic sequences intertwine like an octal helix and ultimately determine the distribution of all prime numbers greater than 5, i.e., starting with 7. It's Archimedean orbits encompass eight arithmetic progressions that double as multiplicative initiators of geometrically expanding period-24 factorization cycles. We explore these patterns in great depth with a powerful analytical tool: a deterministic algorithm and ever-expanding geometry in the form of a spiral sieve (the 'Prime Spiral Sieve'). ![]() Regardless, deciphering how primes distribute in literal, mathematical terms deepens the mystery when you consider the profoundly beautiful algorithms and rotating symmetry groups that govern where on the number line these atoms of the number universe fall. ![]() Any claim to have demystified them, as the title of this work boldly declares, will justifiably be met with skepticism. Prime numbers have been deemed mysterious for more than three millennia.
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