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May 27th, 2017, 12:10 AM  #1 
Senior Member Joined: Dec 2012 Posts: 951 Thanks: 23  Prime's stair and Complicate Modulus
Is very simple to explain with my Complicate Modulus Algebra how Prime Stair works and how Riemann reach it: The basic concept is alway the same: A Clock with More than one Hand, so an Algebra that has a modulus that is a function itself, and non just a number. The Two Hand Clock: This Algebra easy epresent All positive Naturals in fuction of a nth Power of an Integer (hours hand), and a Rest (long, minutes, hand): Chosing for example $n=2$ we have the following Square Strair: To represent the Stair of Primes Riemann find that is necessary to use a Serie to produce the right jump each time a prime born. Since primes are infinite is cler we need a Serie to represent each prime as a zero, so we need an infinite number of Hands in our Clock. Since Naturals are builds by Primes or Composite is clear our clock will produce zeros (when primes) and Rest, when composite. I found in some .pdf around the web that a guy prove Riemann well known himself this fact and spent lot of work to arrive tpo define the right function able to intercept All primes as Zeros. So the concept he use is that we can use an approximated function to define the medium value of the primes, than correct it with a function that intercept each prime. And is clear that a serie that involves all Naturals also contains all primes. I already post here the most simple "function" for primes: $z= n!/n^2$ That works in the same way (as the definition of prime). What is difficoult to understand is the long process take Riemann to build his function. He well known the Complex, that in last instance are another Two Hands Clock , so he use them to produce his zeros dividing them in trivial and non. The question if some zero can lay on a different value of the Real part (so not 1/2) is like asking if a point on a parabola can lay on another point that is out of the equation that define all the parabolas. Is clear that when one doesen't know the answer to a question also doesen't know if his question is right or not. For this reason I ask to math professors to be more relaxed with their students: also a very big mind knowing (very deep) a field of math ...cannot know All, and can say "stupid think" talking of "the unknown", or of the unknown work of a great mind like Riemann (and others)... I've to ask to Abstractist to switch off their fantasy in making new Abstract definition with words / sings that has nothing to do (nor a neuronal connection) with somethink of Real... because math haas always to do with a real think on a cartesian plane... where we, all, learn how to easy figure out our math problems... For example, is waste time to talk of Power of Integers, without knowing what they really are, so from what they are characterized. for sure the magnificent building can give us an answer via abstract algebra, but the way when is to long risk to be unusefull at all.... Last edited by complicatemodulus; May 27th, 2017 at 12:15 AM. 

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complicate, modulus, prime, stair 
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