Talk:Safe and Sophie Germain primes

Untitled

With good intentions, a couple of anonymous users added some redundant passages to the article, repeating some definitions with extremely similar wording. The paragraphs they added on Sophie Germain herself are relevant but make more sense in the article on Sophie Germain. These edits resulted in an article that looked very incoherent. I'm not inclined to question their paragraph on the largest known Sophie Germain prime, but in the interest of detangling the rest of what they wrote I have also taken it out. PrimeFan 15:39, 5 October 2005 (UTC)[reply]

I see it less kindly. Their additions were cut and pasted from Mathworld and other websites, and reworded just barely enough to avoid a red flag from plagiarism detection software. Anton Mravcek 21:10, 5 October 2005 (UTC)[reply]

The proof of Proof was about Sophie Germain primes?

The current version of the article says that:

Sophie Germain primes were the subject of the eponymous proof in the stage play Proof and the subsequent film Proof.

That comes as a surprise to me. I watched the film once, I recall Gwyneth Paltrow's character quoting a large Sophie Germain prime during the party at her house, but I don't recall anything that explicitly said that's what the proof was about. Later on Hal describes it as proving something that people've been trying to prove for centuries, but he doesn't any more detail than this. In general, the movie is not so much about any particular mathematical concept as it is about the psychology of an old math genius and his daughter. PrimeFan 21:45, 5 April 2006 (UTC)[reply]

The film script is at http://www.script-o-rama.com/movie_scripts/p/proof-script-transcript-paltrow-auburn.html. It mentions Sophie Germain primes and later says the proof is about prime numbers, without mentioning SG primes. Mathematically (which may be a poor viewpoint to make speculations about films), it doesn't sound likely to me that the proof should be about SG primes which just aren't important enough, considering what the film script says:

Oh, it's a result, a proof. It looks like a proof. It is a proof. A very long proof. I haven't read through it all yet or checked it. I don't even know if I could check it. But if it's a proof of what I think it's a proof of, it's a very important proof.

What does it prove?

It looks like it proves a mathematical theorem about prime numbers which mathematicians have been trying to prove since there were mathematicians.

You know about this?

- Is it any good?

- It's historic, if it checks out.

What does it mean?

It means that when everybody thought your dad was crazy, he did some of the most important mathematics ever. If it checks out, it means you publish instantly. You hold press conferences. It means that all newspapers around the world are gonna want to talk to the person who found this notebook.

http://www.theaterbarn.org/Page.asp?p=proofshowpage claims the play proof is about SG primes. I haven't seen a play script to confirm this. PrimeHunter 15:28, 29 January 2007 (UTC)[reply]

i get a 404 errror trying to access taht website, so I'm gonna go ahead and delete that statement. Numerao (talk) 16:01, 10 March 2008 (UTC)[reply]

actualy, now that I remeber, they were mentioned in the film. teh only things the dialogue indicates as to teh copntent of the proof is that it proves some longstanding open probem about primes and taht it uses some fairly recent theories to do so. Numerao (talk) 16:04, 10 March 2008 (UTC)[reply]

"Practical Application"

The section about random number generation could use some work.

The section claims that random number generation is a practical application of Sophie German primes, but the section gives no reference for this claim. Using Sophie Germain primes is not one of the mainstream ways to generate random numbers. It is not even listed in Wikipedia's List_of_random_number_generators. If the technique is practical, the section should cite at least one case in which it was used in practice, and give other evidence as needed make it clear that the technique has been established as practical.

Also, the section claims that each digit can be deduced from the previous digit. This is not true (or the example is wrong). Look at the digit '7' in the example. According to the section, the value of the next digit can be deduced merely by the presence of a 7, but in the example, 7 is followed by both 8 and by 3 in the digit stream. Maybe something was lost here in the translation from a mathematical paper to Wikipedia.

Finally, the section should say what is meant by a pseudo-random sequence. Any sequence can be considered a pseudo-random sequence. What is meant is probably that such a sequence produced in the way described in this section has certain properties that are viewed as desirable in pseudo-random sequences. The section should at least cite a reference for this; even better would be to say what one or more of those properties are.

ATBS 03:13, 12 November 2009 (UTC)ATBS —Preceding unsigned comment added by ATBS (talk • contribs)

A quick search reveals that S-G primes are indeed used in pseudorandom number generators. The main paper seems to be this one by Mascagni and Chi in 2004, which has been cited by several other papers on the subject. It argues that S-G primes are well-suited to distributed random-number generation via linear congruential generators, because they greatly reduce the initialization time (to find the generators of the multiplicative group) compared to Mersenne primes. (That being said, this appears to still be a recent technique and perhaps not all that widespread yet.) — Steven G. Johnson (talk) 23:53, 12 November 2009 (UTC)[reply]

Very interesting. I still stand by my comments. Incidentally, in the Mascagni and Chi paper, it appears that they are not using Sophie German primes as described in the section of this wikipedia article. They are selecting Sophie German primes and then using these primes in a different kind of generator (linear congruential generator). ATBS 10:59, 13 November 2009 (UTC) —Preceding unsigned comment added by ATBS (talk • contribs)

New record

According to primegrid a new record SG prime has been found, April 2012. Bubba73 ^{You talkin' to me?} 00:02, 18 April 2012 (UTC)[reply]

I have updated the article.[1] PrimeHunter (talk) 22:41, 18 April 2012 (UTC)[reply]

Name

It would be nice to find some information on why the name "Sophie Germain prime". In particular:

Normally, when something in maths or science is named after somebody, only the surname (or mononym, in the case of ancient Greeks) is used. So why this exception? (Possibly because in later life she wanted to emphasise her gender in order to show that women can be great mathematicians?)
For it to be named after Sophie Germain, presumably she studied them. But what drew her attention to primes with this property? What did she discover, or try to discover, about them? — Smjg (talk) 23:48, 2 June 2012 (UTC)[reply]

See Sophie Germain#Best work on Fermat's Last Theorem. PrimeHunter (talk) 21:28, 3 June 2012 (UTC)[reply]

merge

Do we need safe prime as a separate article? These are rather like twin primes. It's true in this case we have separate names for the upper and lower prime, but mathematically they go together. --99.238.163.176 (talk) 17:05, 11 April 2019 (UTC)[reply]

I agree, having two articles is silly and they should be merged. --JBL (talk) 14:44, 17 June 2019 (UTC)[reply]

I'm ok with a merge as well. Both names are useful, but not independently notable, and the one here is the better known of the names. —David Eppstein (talk) 20:21, 17 June 2019 (UTC)[reply]

Oppose. Sophie-Germain prime may be the most known term in pure mathematics (I wouldn't know), but it is certainly not a common term in the technical discipline of cryptography, where the known terms are "safe prime" (with thousands of bits) and "strong prime" (with thousands of bits) and well-sourced text is needed to state which is which and for what use independently from general discrete math, such as large and small decimal primes or historical relationships to work on Fermat's last theorem. The math overlaps, but the practicalities are as unrelated as mathematical cylinders versus structural pillars. Jbohmdk (talk) 20:23, 8 September 2019 (UTC)[reply]

Given this objection, perhaps it would be possible to have a page name which includes both; perhaps Safe and Sophie Germain primes, partially by analogy with Coprime integers (page discussing number pairs) and twin prime (where prime pairs are discussed). Klbrain (talk) 17:40, 8 April 2020 (UTC)[reply]

Merger complete. Klbrain (talk) 09:18, 27 June 2020 (UTC)[reply]

Une curiosité

(53) est une unité de Z/210 et 53 est un germain. Considérons alors l'inverse de (53) dans Z/210 : c'est (107). Considérons alors la suite arithmétique de premier terme 107 et de raison 210: elle fournit au moins 6 jumeaux, à savoir (107,109), (1787,1789), (1997,1999) et (3257,3259), (3467,3469, (4517,4519)... En 1787, Sophie Germain avait 11 ans et 13 ans en 1789. La dernière partie est sans doute une coïncidence mais la première ne correspondrait-elle pas à une propriété des germains ou d'objets mathématiques associés qu'il serait heureux de voir figurer dans wp? Cordialement et bon casse-tête.--Stefan jaouen (discuter) 18 août 2019 à 17:49 (CEST) — Preceding unsigned comment added by Stefan jaouen (talk • contribs) 16:10, 18 August 2019 (UTC)[reply]

Wiki Education assignment: Number Theory I

This article was the subject of a Wiki Education Foundation-supported course assignment, between 22 August 2022 and 12 December 2022. Further details are available on the course page. Student editor(s): AlizianaE (article contribs).

— Assignment last updated by AlizianaE (talk) 11:56, 9 December 2022 (UTC)[reply]