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2020-10-10, 13:40   #1
paulunderwood

Sep 2002
Database er0rr

3,533 Posts
Prime Numbers Book

Enjoy and criticize. It ain't no C&P but might help some.

2 More downloads and I have uploaded a new version without the Euler Phi Function nonsense -- Thanks Robert.

24 more downloads and a new version is up with accumulated corrections and suggested text.

13 more downloads. The replacement (12th Oct) version corrects some grammatical errors, includes suggestions by Nick and a Lucas Sequence algorithm.

12 more downloads. The replacement (Oct 15th) makes the suggestions by Nick and corrects some typos.

4 more downloads. The replacement builds on suggestions by Nick. There is now a section on Gaussian primes. Replacement (18 Oct,2020) uploaded.
Attached Files
 Prime_Numbers_by_Paul_Underwood.pdf (191.2 KB, 43 views)

Last fiddled with by paulunderwood on 2020-10-18 at 00:19

 2020-10-10, 14:10 #2 Dr Sardonicus     Feb 2017 Nowhere 3×7×199 Posts There is a caveat in using the term "number" to mean "natural number" or "positive integer." Euclid distinguished between 1 ("the unit") and integers greater than 1, which he called "numbers." Thus, a "prime number" was, by definition an integer greater than 1. The unit, 1, is neither prime nor composite.
 2020-10-10, 14:28 #3 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 37×131 Posts spell check; grammar Legendre, Jocobi and Kronecker (should be Jacobi) (page 3) "The determinant of a A is" (bottom of page 9) The determinant of a matrix A is nothing else conspicuous through page 10 on a first pass. Pretty clean. Last fiddled with by kriesel on 2020-10-10 at 14:29
 2020-10-10, 14:52 #4 Viliam Furik   "Viliam Furík" Jul 2018 Martin, Slovakia 2×167 Posts Page 3 - Typo in "Jocobi" Page 32 - Fig. 7.1 contains n = 2 twice, lots of unknown where it shouldn't be (n= 61,89,107)
 2020-10-10, 15:59 #5 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 26258 Posts On page 39: "The Euler Phi Function is useful since for all a a^(1+φ(n)) ≡ a (mod n)." This is very false, a small counter-example is a=2, n=4.
 2020-10-10, 20:46 #6 bhelmes     Mar 2016 33×11 Posts "It is important to analize the the exponentiating" page 49. Greetings Bernhard
 2020-10-10, 20:53 #7 Knut   Oct 2020 210 Posts You write i were the square root of -1. As far as I know, the square root r of a number x is the non-negative solution of the equation r^2 = x as far as real numbers are concerned. As i is neither positive nor negative and i^2 = -1 and (-i)^2 = -1 in my opinion it is not correct to say i would be the square root of -1. Best regards Knut
2020-10-10, 22:40   #8
paulunderwood

Sep 2002
Database er0rr

3,533 Posts

Quote:
 Originally Posted by Knut You write i were the square root of -1. As far as I know, the square root r of a number x is the non-negative solution of the equation r^2 = x as far as real numbers are concerned. As i is neither positive nor negative and i^2 = -1 and (-i)^2 = -1 in my opinion it is not correct to say i would be the square root of -1. Best regards Knut
I have read https://en.wikipedia.org/wiki/Imaginary_unit What would you say I should write? i is fixed to be one of the two square roots of -1?

Last fiddled with by paulunderwood on 2020-10-10 at 22:44

 2020-10-10, 22:43 #9 paulunderwood     Sep 2002 Database er0rr 3,533 Posts I have tidied up what I want write about "The Fermatian Child". I will refrain from reposting the paper until more input from folks. Last fiddled with by paulunderwood on 2020-10-10 at 22:51
 2020-10-11, 05:28 #10 Knut   Oct 2020 210 Posts I think there is no square root of -1. Instead, define the "imaginary unit" i with i^2 = -1. And then define complex numbers. This, in my opinion, could help to avoid disturbances. E.g. x^2 = 3*i x^2 = - 3*i x^2 = 2 + 3*i x^2 = 2 - 3*i x^2 = - 2 + 3*i x^2 = - 2 - 3*i There are two (complex) solutions of each equation, of course. Which of the two solutions is to be named the "square root"? I am not aware of a definition. I apologize fpr my poor command of the English language and hope you can see my point. Best regards Knut
 2020-10-11, 07:44 #11 Nick     Dec 2012 The Netherlands 3·17·31 Posts There are a number of errors at the start, some just details of definitions but others hiding more important points. How it would be best to resolve these depends strongly on who you are writing this for. What is the intended audience?

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