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

http://www.bbc.co.uk/h2g2/guide/A660287

This is an entry explaining about Mersenne Numbers and the search for large Mersenne Primes.

There's a single occurrence of first person here: 'I'll present this in the form of...' but that's all there is to the negative side.

Just asking...: didn't the sieve of Erasthenes play an important role sometime in the history of prime numbers? Or perhaps, it doesn't have anything to do with Mersenne primes.

thumbs up, Gnomon

Thanks, Bossel. I'll fix that first person ref. I don't know how that slipped in. There is a lot more I could say about prime numbers, including the Sieve of Eratosthenes and actually providing Euclid's proof of the infinitude of primes, but the article is really about Mersenne primes.

Hi, few things I noticed:

I think the smileys have to go, even though theyre being a useful visualisation. I had to remove them from 'Bigger and Bigger Infinities'. You can maybe do something similar using tags and *s.

Proof by contradiction is outlined in 'Basic Methods of Mathematical Proof', which is A387470.

"For those of you who don't understand formulas..." seems a little condescending, maybe you could change it to something like "if formulas are all Greek to you,..."

"It is now easy to see that this is divisible by 111" ...because it is 111*001001001001001 - would be clearer.

"only the following Mersenne numbers are prime: " You mean those beyond the ones we already have? M_17, M_19 etc?

Good stuff. Why isnt there an entry just on primes yet?

Thanks Henry. I'll try and make the changes you have suggested later today.

I've made those changes now.

Hi Gnomon,

This entry is excellent. Explained really well. Just one thing in terms of style, and it's a small point.

You present the x^2 + x + 42 formula really well, taking care to bring non-mathematical people with you, but then two paragraphs down you introduce Lucas / Lehmer's method with no mathematical safeguards in place. You might lose non-mathematical people unless perhaps you can show a simple example of what you mean. For instance, the concept "Modulo" (only taking the remainder after a division?) is not explained.

As I said, it's a small thing.

Woodpigeon

Nice entry! I have three comments.

1. Thanks for the biographical info. That's too often neglected in Maths. You don't happen to have Lucas' dates, and Lehmer's first name and dates, do you? I'm always interested in the people behind the math, y'know. Ooh, Fermat, too. (And A521966 is about his last theorem, which is only tangentially related...)

2. http://www.bbc.co.uk/h2g2/guide/A600427 is an Edited Entry which explains about the binary system. Might be a good link.

3. Talking about modular arithmetic without explanation is a bit intimidating for the uninitiated, I'd think. Not that I can think how you'd explain it in less space than another entry. (note to self: write that entry...)


I hope they give me this one to Sub!



GTBacchus

Great entry.

You don't explain what Modulo is, this might confuse the lay readers.

Nothing more to add here.Recommended by me.

Changing subjects, and initiating an excursus:

How are prime numbers connected to dimensionality? Do you know anything about that? Prime vectors (scalar product please!) I was wondering the other day (while reading Mandelbrot - of course) if the prime numbers are nothing but an artefact of 1-dimensional analysis of the problem. Maybe you find a fractal dimension, where prime numbers follow a rule. Is that too absurd? To illustrate what I mean:

Normal (1 dimensional) maths:

1 + 1 = 2 (or: 1^1 + 1^1 = 2^1) BUT

1^0.5 + 1^0.5 NOT= 2^0.5 (= 1.414...).

OR:

2*5^x = 11 when x=1.05922...


Well, must be the insomnia...

HELL

PS: Is it true that Euler was blind and calculated all his stuff all in his head?

Hi Gnomon,

Excellent entry, and reasonably clear. I'd just like to make two suggestions.

The first is the phrase
Afterwards he admitted that it had taken him "three years of Sundays", that is, over twenty years of work, to find the result

I could read that in two ways, the way you explain, or the fact that he worked every Sunday for three years on the project - are you certain that you have the right meaning

Secondly,

Is there any way that you could change the layout of the text so that the passages with large numbers in them are clearer to read? Perhaps with the all the figures on the left hand side of the page and the comments to the right

I threw together a quick table, which gives you the general idea of what I'm going on about.


(And in case your having a heart attack about the idea of sticking all that in table format. The whole thing took me about 3 minutes of copy/paste using MaW's GuidePost Programme, with its nifty little table builder)

MaWs page is here, to download the GuidePost programme:
http://www.bbc.co.uk/h2g2/guide/U55669
and my pathetic effort at formatting is here:
http://www.bbc.co.uk/h2g2/guide/A664157

PS. Please feel free to tell me to get stuffed if you think that it'd be too much work.... It wouldn't stop me recommending this one


whisky

I don't know if you want to include it, but as well as publisising information for general distribution, mersene would also publish information that he was asked to keep private pending confirmation.

as you can imagine, this sometimes made him unpopular.

Thanks for all your comments.

I've added dates for the various mathematicians. I'm still investigating Lehmer but will probably know his name and dates by tomorrow.

'3 years of Sundays'. I've removed the explanation and leave you to draw your own conclusions as to what he meant.

I've added a blow-by-blow description of what (u^2 - 2) modulo Mp means.

Whisky, I see what you mean about the layout of the paragraph with all the 1's in it, but I don't like the look of your table. It is equally unreadable in my opinion. If anyone else has a suggestion for the formatting or rewriting of this paragraph, I'd like to hear it.

For biographical research on mathematicians, you can't do better on the web than the St. Andrews history of mathematics web page, there's a link on my userspace.

Also, on the "Formula for prime numbers" section, you might want to mention an interesting and little known "formula for primes". It is a massive polynomial p(a,b,c,...,z) in 26 variables. It doesn't always produce prime numbers, but whenever it is positive it is prime, i.e. if p(a,b,c,...,z)>0 then p(a,b,c,...,z) is prime. Unfortunately, it is almost always negative, and so it isn't very useful for producing primes. I can dig out a page about it if you like?

Thanks Dogster. I think the "formula" sounds interesting and I would like to see it at some stage, but it will only scare people away from the Entry so I won't include it there.

My problem with Lehmer is that there were two Lehmers, a father and son, and both were involved in Number Theory. I haven't yet figured out which one it was that made the modifications to the Lucas test. I'll check out my maths books when I get home.

"If anyone else has a suggestion for the formatting or rewriting of this paragraph, I'd like to hear it."

One possibility would be to use smaller numbers. Instead of M15 and M35, you could use M6 and M10, and the demonstration would not diminish in effectiveness, I think.

The way I handle formulas is to separate them from the rest of the text in little paragraphs of their own. Gnomon, you were at:

http://www.bbc.co.uk/h2g2/guide/A662474 - The Great H2G2 Researcher Count

...the other day, but I've written a lot more, and you might check it out again. If it's very readable, it might give you some ideas (feel free to code), and if it's not, please tell me so. Actually, I'd really appreciate feedback from anyone.



"Similarly, M35 can be written 11111111111111111111111111111111111 but since 35 = 5 * 7, this can be written 11111,11111,11111,11111,11111,11111,11111 which is clearly divisible by 11111"

could perhaps be rephrased "Similarly, M35 can be written as a string of thirty-five '1's, but since 35 = 5 * 7, etc", maybe.

Cool entry. I agree with GTBachus. Use smaller numbers. It's even more effective.

!

I've added Lehmer's dates (it was Derrick Henry Lehmer, the son and inventor of the electromechanical prime sieve).

I've changed the section with all the ones to show the divisibility of M6 and M10 instead of M15 and M35. You're right! It does look a lot more readable.

Thanks everyone.

I liked this entry, even though I`m not that interested in maths and less so in prime numbers. Finding the largest prime number seems akin to finding the highest mountain and then climbing it. Why? No reason, just because its there!
No one has found a formula for prime numbers yet? Thats truly amazing, given how long we`ve been studing primes...
Also, it reads better now that some changes have been made and I would recommend it.

Hi

I liked this too, and I am a maths *dunce*! The introduction to prime numbers works really well as does the bio. I have to admit, I got a bit lost with some of the formula stuff.

I think I did correctly work out what it meant, but this sentence took me a bit by surprise - "where did that M come from?' I thought to myself. "And what is that 2 doing down there?"

Speaking of formulae, I am comfortable with 'formulas' as the plural form, but is it an issue in maths? Do some people use the -ae form or is it passing out of usage among the scientific community? Pure linguistic interest.

Anyway, I was pleasantly surprised (not just a number dunce, a *number-ist* too) to find a very approachable, informative and readable article. Thanks

Spiff