20201010, 13:40  #1 
Sep 2002
Database er0rr
3,533 Posts 
Prime Numbers Book
Enjoy and criticize. It ain't no C&P but might help some.
After 20 downloads, I have made the changes to typos and Mersenne data. A new copy is now uploaded. 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. Last fiddled with by paulunderwood on 20201018 at 00:19 
20201010, 14:10  #2 
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. 
20201010, 14:28  #3 
"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 20201010 at 14:29 
20201010, 14:52  #4 
"Viliam Furík"
Jul 2018
Martin, Slovakia
14E_{16} 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) 
20201010, 15:59  #5 
"Robert Gerbicz"
Oct 2005
Hungary
1429_{10} 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 counterexample is a=2, n=4. 
20201010, 20:46  #6 
Mar 2016
451_{8} Posts 
"It is important to analize the the exponentiating" page 49.
Greetings Bernhard 
20201010, 20:53  #7 
Oct 2020
2 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 nonnegative 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 
20201010, 22:40  #8  
Sep 2002
Database er0rr
DCD_{16} Posts 
Quote:
Last fiddled with by paulunderwood on 20201010 at 22:44 

20201010, 22:43  #9 
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 20201010 at 22:51 
20201011, 05:28  #10 
Oct 2020
2 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 
20201011, 07:44  #11 
Dec 2012
The Netherlands
62D_{16} 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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