Talk:Pseudoprime

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Rasta, I would really appreciate it if you didn't cause me more work than necessary. Do I really have to justify every edit on Talk so that you don't revert it? Ok, here we go:

This table

Fermat's little theorem gives us for the first numbers:

n an-1-1 an-1 -1 mod n
1 0 0
2 1 1
3 3 0
4 7 3
5 15 0
6 31 1
7 63 0
8 127 7
9 255 3
10 511 1
11 1023 0
12 2047 7
13 4095 0
14 8191 1
15 16383 3
16 32767 15
17 65535 0
18 131071 13
19 262143 0
20 524287 7
21 1048575 3
22 2097151 1
23 4194303 0
24 8388607 7
25 16777215 15
26 33554431 1
27 67108863 12
28 134217727 7
29 268435455 0
30 536870911 1
31 1073741823 0
32 2147483647 31
33 4294967295 3

is completely unintelligible. You don't say what a is; apparently you use a = 2. Furthermore, Fermat's little theorem says that the third column should always be 1, so obviously it wasn't used, contrary to the claim.

I removed the | symbol for division because the rest of the article uses "divides".

I removed the Moebius function values since they don't provide any insight here. What point to you want to prove by including them. Sure it is an arithmetical function, but there are dozens of other arithmetical functions, why didn't you add information about σ(n) and φ(n)? It is pointless; there is no connection that needs to be mentioned. Furthermore, anyone interested in the moebius function can easily find the value, since all they have to do is to count the prime factors, which are already given in the table. In the final paragraph, formulating the (false) conjecture in terms of prime factors makes it much easier to read to the non-specialist.

I removed the link to the super-Poulet integer sequence entry because it belongs on the article about super-Poulet numbers, not here.

I also removed "We do not calculate numbers 2n-1. " because I have no idea what it means. AxelBoldt 16:04 Sep 25, 2002 (UTC)

(1) I really do not want to cause anyone more work than necessary. But I can't help if someone try to suit every single article to his own fashion. You just throw out everything that does not fit to your personal view. Try to edit articles more for the reader and not for yourself. What is wrong if one sentence is not quite adequate and explicit. On the other hand I am doing my best to compose one article from the scratch and then you come and you 'ruin' almost my whole work. Who is doing fruitless work here? You're obviously to deep in the math and you can't see out anymore. Try to read one original work from an original mathematician, please. If you would have a chance, you would probably change even Gauss' work. Remember on what he had written about the estimation of the number of primes and such.
(2) I'll try to fix the table, that bothers you so much. (Just give me some time).
(3) Don't call me Rasta if you're not shure what that means or if you think I am that, if I bear similar cyber nickname, and so on :)
(4) The symbol |. Sometimes you like and sometimes you don't. For instance it is more clear if we write, once we have agreed what | means, 3 | 9, than 3 divides 9. You have once said that any symbol in fact does not have much sence in math so here we go...
(5) What is wrong with Möbius function here or elsewhere. When I make a table, it is clear after that what values are, but try to 'calculate' its values from your mind. I gave the function to depict further on the whole subject. It is pointless; there is no connection that needs to be mentioned. That is you opinion, I guess. Everything is important in math, specially in a number theory. If I wouldn't use Möbius function I wouln't be able to find those two numbers 648 and 700. I guess here μ(n) is 'more' important than other arithmetic functions. That's my opinion. Furthermore, anyone interested in the moebius function can easily find the value, since all they have to do is to count the prime factors, which are already given in the table. Yes, that is true. But many readers do not know at first what μ(n) means and shows. Simply as that.
(6) I am not your student out there somewhere so we have to work for this project. You correct me and I correct you if and only if I can. I am pretty tired of writting articles which envolve math, but I like math very much. And because you know something from the math, you can give your knowledge to others and not just fixing things all around as it is going for one math test. My teachers are mathematicians themselves. Only you change these articles so much, no one else. So I can't figure that they do not understand what is written in them. Egziabeher. --XJam 17:20 Sep 25, 2002 (UTC)


Rasta-kun:

1) Your table header had an error. You wrote this: an-1 mod n instead of this: an-1-1 mod n. I fixed it.

Thank you. Yo ad ustay an neh ah ukob.

2) Why not write "9 mod 3 = 0" for "3 divides 9"?

Or 9/3=3+0:) --Nuk-ta-fire-sar [2002-09-25] 2T.

--User:Juuitchan

Try to edit articles more for the reader and not for yourself. What is wrong if one sentence is not quite adequate and explicit.

I edit for the reader, and unclear sentences are therefore changed/removed.

The symbol |. Sometimes you like and sometimes you don't.

If you tell the reader what it means, you can use it. But this article uses "divides" throughout, so it doesn't make sense to start using | all of a sudden in the middle of the article, without explanation.

It is pointless; there is no connection that needs to be mentioned. That is you opinion, I guess.

Indeed. And unless you can point me to some interesting connection, some theorem or even conjecture involving pseudoprimes and μ, there is no point in mentioning the μ function here.

But many readers do not know at first what μ(n) means and shows.

Right, and they don't need to know it, since it doesn't have anything to do with the topic at hand. AxelBoldt 18:20 Sep 25, 2002 (UTC)


Where does the table with the smallest pseudo primes come from? AxelBoldt 22:52 Sep 25, 2002 (UTC)

The table is entirely my calculation, so do not worry. It took me nearly 3 hours to calculate. The previous one I gave was slightly wrong as probably you have observed. You can throw it away if you don't like it - as you wish :) or as you wrote that "intellectual property rights" does not exist. This is my opinion too. -- XJam 01:07 Sep 26, 2002 (UTC)
How could a person own the rights to mathematical equalities? User:Juuitchan
Most probably he can't. -- XJam
Do you use Maple or Mathematica or some such program? AxelBoldt 01:15 Sep 26, 2002 (UTC)
Strictly Maple (V Release 4.00a). I've made all functions by myself for that particular table, so we can see how Maple is strong. And my knowledge of programming is somewhere in the middle. I have tryed other programmes, but I like Maple the most. --XJam 02:23 Sep 26, 2002 (UTC)

I think the bold terms all need to appear in the first few lines. I arrived here expecting Poulet numbers and was completely befuddled until the fifth paragraph. --Omphaloscope 19:14, 8 Apr 2005 (UTC)

[edit] Proposed reorganization

I'd like to see a separate article on Fermat pseudoprimes (and its close friends). I think pseudoprime should mainly define the general concept and link to the many types of pseudoprimes, almost like a disambiguation page. I'll make this change if there's no objection. Deco 01:07, 9 Apr 2005 (UTC)

First: I am User from the german Wikipedia. I would like to concentrate the Fermat Pseudoprimes to the Euler Pseudorimes, because the important Fermat Pseudoprimes like Poulet Numbers, Cipolla Pseudoprimes, Carmichael Numbers, Zeisel Numbers, (6n+1)*(12n+1), ... are Euler Pseudoprimes. The rest, like 15, 35, 52, 66, 70, 85, 87, ... are less to unimportant. --Arbol01 01:38, 11 Apr 2005 (UTC)

[edit] How are they named?

How is a number of the Form a^{2(n-1)} \equiv 1 \mod n for every \operatorname{gcd}(a,n) = 1 named?

And how is a number of the Form a^{2^m(n-1)} \equiv 1 \mod n for every \operatorname{gcd}(a,n) = 1 named? --Arbol01 11:42, 30 July 2005 (UTC)

[edit] Reverted back

I re-reverted to the version produced by 71.241.234.207 because in my opinion this version is more accurate than the version proposed by User:EJ. -- Bob.v.R 14:11, 17 April 2006 (UTC)