Prime as a Mathematical Operator 9798702626949

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Prime as a Mathematical Operator. (c) 2021 Ahmad Chamoun

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Dedicated to my students.

Introduction

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This the first of a three series collection aimed at making a simple unified math curriculum. The second book will be no more than 20 pages and should be done in a few months before schools reopen. As a substitute teacher I only have an hour at most with my students and thus it makes sense for me to make as condensed and simple a curriculum as possible. I am aware dear reader that with you I only have less than five minutes so lets get started. More lengthy computations will be reserved for the third publication which will explore possible mathematical constraints introduced in asterisks towards the end of this publication on page 9.

The Concept

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The proof begins with a simple observation. I realized some time back that if you take the number 18 and multiply it by itself you will get a result that is always divisible by nine. Likewise if you take the numbers 108 or 1008 or 1000000008 you will achieve a similar result. Moreover if you look at the products of such multiplication they build off of each other. For convenience I have included the results on the next two pages. They aren't as clear as I would have liked and I don't remember where I kept the originals so don't worry to much about detail the point is that the results are building off of one another, if you add the digits next to each other they produce the ones after in the higher iteration. Let me provide an example. For the products of 10008^9 and 100008^9 which are 10072230830.., 10007202304430… respectfully you can see where the two 4s split off of the 8. Also all the products are always divisible by 9.

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My original intention was to develop a math game for my students where they compared the cards and results of each multiplication to figure out which ones contained similar strings of digits and for every time someone was able to demonstrate an addition the type of which I proved earlier they would score a point. My intention was to make get them used to big numbers so that they wouldn't be afraid of them when

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doing math. While doing research for this game I stumbled upon a very interesting mathematical property and that is what my main thesis is about.

After I got to the iteration with 8 zeros, 1000000008 I realized that if I added one and divided by 449 I yielded an extremely large prime number, a larger one wasn't discovered until right before WW1. But why was it prime? The reasons for this is because of satisfying certain properties in what I like to call the preprime test. 18 is special because 8+1=9 which is half of 18. No other number in base 10 has this property.

((1000000008^8+1)/449)=22271716347438792694878144 14254536124725690440996302966629793354157633.

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The Formula

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But by no means is math limited to base 10. We can use any base that we desire. Thus we can discover as many primes as we desire. The higher the base, the bigger the prime. I hypothesize that all that needs to met are some criteria in seven steps. 1) A. Find a number such as 18 whose representation if added as integers equals half of the original number (1+8=9) half of 18 and B. whose exponents are always divisible by half of it (in this case 9). 2) *Certainly a number in some base exists that is more than 2 digits a topic to be explored in the last book of the series* 2) Place the exact amount of zeros between both numbers. (In the case of 18 we must place eight zeros between 1 and 8) 1000000008 3) Raise the number which you now have the power of the amount of zeros which you added. 1000000008^8 4) Add one. *(It may be possible that 1 needs to one of your numbers from step 1, in our case we had (1+8) * ((1000000008^8)+1)) 5) Subtract one from the

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original number that you found in step 1 (18-1=17) 6) Break this number down into another number whose integer representation is equal it while satisfying the criteria that the split is preformed equally. (17–>449) 4+4+9=17. *(notice that 10-1=9 and we are in base 10 this may also be a constriction, also all of the exponents of 18 and 1008 1000008 ect are divisible by 9)* 7) Take the expression from step 4 and divide it by the number from step 6 and now you have a prime number.

Conclusion In my free time I will try to find bases that fit this formula and publish the results in my third book. Also I will deal with small primes such as three and try to fit those into the working formula. Until then it is definitely possible that someone else build on this work and find large primes themselves. The point I want to get across is that primes can be constructed from certain criteria that match that of mathematical

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operations such as division, addition and multiplication. Just as multiplication is an extension of addition, I propose that primeness is an extension of these also (recall that subtraction is a special form of addition and division of multiplication). Thus primeness is better defined as a mathematical function in and of itself. A definite proof in other bases will not be made available until the third book unless, as I'm hoping someone else beats me to it.

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