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Old 2012-12-13, 18:31   #1
skan
 
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Default compendium of formulas related with primes ?

Hello

I'm looking for a book with a compendium of formulas related with modular arithmetics, Wilson's theorem, Fermat theorems, diophantine equations, number field sieve, and other not so well-known, and maybe elliptic curves and algorithms such as Miller-Rabin....

I've seen that some typical Formulae books contain very little about this subject.
(Zwillinger, Bronhsteid, Weisstein, Polyanin, Abramowitz...)
And all "number theory" books I found are too theoretical, plenty of demostration but not a summary of relations.

Another option would be some computer/cryptography texts but they don't include many formulas either, and they spend most of its pages with computer related things and long explanations.


Could you suggest me any book or link, please?
I mean, I would like to have in a book or pdf a summary of all known relations containing prime numbers and modular calculus.

regards

Last fiddled with by skan on 2012-12-13 at 18:33
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Old 2012-12-14, 01:14   #2
science_man_88
 
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Quote:
Originally Posted by skan View Post
Hello

a summary of all known relations containing prime numbers and modular calculus.

regards
if you mean like statements containing \equiv maybe too many exist to fit in a reasonable sized file, Fermats little theorem,Wilson's theorem, Euler-Jacobi pseudoprimes, and facts like the primes can only reside in modular classes that are coprime with the modulus. and there's a lot more like these at last check.

Last fiddled with by science_man_88 on 2012-12-14 at 01:15
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Old 2012-12-14, 01:51   #3
jasonp
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That's actually an interesting question; you need a desk reference if you just want to use results in (say) applied mathematics without understanding where they came from, but in what field can you claim to need that with number theory? You can list algorithms for (say) modular exponentiation, and there are many of them, some very complicated, but a list isn't very useful if you just want to read the list and not do anything with them. Even in that case you can look up the relevant chapter in the Handbook of Applied Cryptography.

On the other hand, how do you summarize a subject that is as old as mathematics itself?
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Old 2012-12-14, 02:00   #4
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The books I listed above contain more than 30000 formulas.
Then I think it's possible.
The problem is that the formulas I'm asking for could be considered too specific or complicated or not interesting for most people.

I know that many of them area contained in some cryptography books, but they spend 99% of the space with long explanations, comments and non related subjects.

Last fiddled with by skan on 2012-12-14 at 02:03
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Old 2012-12-14, 03:11   #5
LaurV
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Quote:
Originally Posted by skan View Post
but they spend 99% of the space with long explanations, comments and non related subjects.
Ha ha ha... indeed?!? To get the best ratio between what the reader expects when he start reading a book and the real content of the book, we should only read sandra brown's books.... (edit: and listen only to justin bieber's songs).

Last fiddled with by LaurV on 2012-12-14 at 03:13
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Old 2012-12-14, 12:37   #6
henryzz
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One book that might be worth looking at is Crandall and Pomerance's 'Prime Numbers: a computational perspective'

This might be over the top mathsy for you.

Last fiddled with by fivemack on 2012-12-14 at 19:16
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Old 2012-12-14, 12:56   #7
skan
 
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Quote:
Originally Posted by henryzz View Post
One book that might be worth looking at is Prime Numbers: a computational perspective by Crandall and Pomerance.

This might be over the top mathsy for you.
Thank you henryzz

Last fiddled with by fivemack on 2012-12-14 at 19:17
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