h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I like this entry. I find it interesting. I note that it does not seem to technical for those without much knowledge of maths, without appearing patronised.

I have a few comments to make;

You say that

"A number which can't be divided evenly by any other number (except 1) is called a prime number"

You should probably mention that a prime number must be greater than 1, and must be an integer (a whole number), and that it is allowed to divide evenly by itself, as well as by 1. This is important, as if 1 is considered a prime, then a composite cannot be uniquely defined as a product of primes. For example 6 = 2*3,6=2*3*1, and so on. The number of 1's involved does not change the product.

You also say that to check if a number is prime, you need to check all the odd numbers up to the square root. In fact, you only need to check the prime numbers up to the square root. It would still take a long time to check whether large numbers were prime using this shortcut, but not quite as long.

You say later than there was no way of mathematicians communicating results to each other. This would not, I imagine be strictly true. However, it would be true that there would be formal, organised way of communicating results.

You mention Euclid proof of the infinite number of primes, and describe this as an example of "Reduction to Absurdity". I think that it is more often known by the latin name "Reducio ad absurdum". It might also be interesting to give Euclid's proof, as it is fairly simple, although finding a link to the proof might be better.

You also mention the RSA public key, private key system. It might be worth briefly saying how it works. Not the full details, just a brief note about how primes are involved.

OK, ask a non mathematical person, I followed a lot of this entry, (quite an achievement) except the formula in the middle 'Set U = (U2 - 2) modulo Mp'. What does modulo mean? And what's the Mp?

'modulo' means you divide the number to the left by the number (Mp) to the right, and throw away anything apart from the *rest*

So, 13 modulo 5 = 3; and 10 modulo 5 = 0

Thanks for your comments, everyone.

Spiff, you say "this sentence took me by surprise", but you don't say which sentence you are talking about. Can you be more specific?

Formulae is still sometimes used, but formulas is common and seems less offputting to non-mathematical readers.

Silverfish,

Your points are all valid, but I am not trying to produce a rigorous definition of prime numbers. The article is supposed to be about Mersenne Numbers. I'm trying to give the absolute minimum understanding to get through the article. I don't want to scare the non-mathematical people off.

I do actually say that primes can be divided evenly by themselves, because I say "can't be divided evenly by any _other_ number". I admit that I don't specifically mention negative numbers, non-integers or 1 itself, but interested parties will probably get by without a list of all the exceptions. I know that reductio ad absurdum is more normal, but many readers do not speak Latin, so I have translated it.

My check for primeness is the simplest, not necessarily the quickest. It is much easier to divide by a load of odd numbers than to create a table of primes and divide by each of those.

Singing Fish,

The sentence you found difficult, the one with the modulo in it, is explained clearly about two lines further down.

Oops, sorry about that. I meant the following sentence:

>>He quickly found that if n is not a prime, then Mn is not a prime.

Now, I assume that M = 2n -1 mentioned directly above. However, this 'M' is not specifically defined as such. I also wondered why the 2 had dropped down below the line - it looks like 2 molecules of the chemical M!

When reading the thread here it occurred to me that you might simply create a new entry entitled something like 'Prime Numbers', cut and paste much of your intro into this new entry and link to it in your Mersenne entry. Then you have all the time in the world to produce a more rigourous article about Prime nos afterwards. You may still need a brief description of prime nos in your intro but it would take up less space and would allow a curious reader to gen up on the details if they choose. Just an idea.

Spiff

Spiff, I see what you mean. I had actually introduced the Mn notation at the very start of the article, where I said Mathmeticians write M7 = 2^7 - 1. But if it is not obvious to you, then I need to make it clearer. I've added an extra line to explain at the point where you were surprised.

Hi, just reread the intro where you do make it perfectly clear about the M_subscript_n system for depicting Mersenne numbers. I guess it was taking in all the stuff about prime numbers in between that caused it to completely slip my mind.

Looking at the change, it occurred to me that it was much clearer for *us* non-maths people but perhaps rather heavy-handed to others. To be honest, I wouldn't want you to break up the flow of your entry for my sake.

Dear me, there's just no pleasing some people, eh!

Editorial Note: This conversation has been moved from 'Peer Review' to 'Mersenne Numbers'.

This thread has been moved out of the Peer Review Forum because your entry has now been recommended for the Edited Guide.

You can find out what will happen to your entry here: http://www.h2g2.com/SubEditors-Process

Congratulations!

Thanks!

Azara

Nice one!

Spiff