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

Thanks. I'll reread it tomorrow, I'm too tired (i.e. unconcentrated) now. I searched for the name of the book but couldn't find anything.

I've been looking as well, to no avail. Might have to look at my O.U. video on 'Music of the Primes' to see if that mentions it. Still need to puty in that table, which I've been putting off .

If I find something I'll tell you.

It was a book of logarithms (Just found it

Just about to start constructing the table

with that.

Done my table .

It would look better if I could put a grid around it, but I don't know whether this is possible ...

Entry: Prime Numbers - A25209047
Author: Big Al - Member, Wessex Researchers Group, Keeper of Mnemonics, Patron Saint of Left Handers - U723247

A grid? That's a bit more than guide ml for beginners, I guess. I'll look for the code tomorrow, I know it can be done, I'll find out how.

Hi, BigAl!

This is a good entry, but there are a few mistakes in it which I'd like to see you clear up.

Content

1.

"It can be shown that all composite numbers can be produced by multiplying prime numbers togethers.
This is now a theorem known as the 'Fundamental Theorem of Arithmetic', also called the 'Unique Factorization Theorem'."

No, that's not right. It's pretty trivial to show that all composite numbers can be producted by multiplying prime numbers together. What the Fundamental Theorem of Arithmetic, also known as the Unique Factorisation Theorem, says is that for each composite number, there is one and only one set of prime numbers which will produce it by multiplication. So for example, we can't N = a * b = c * d where a, b, c and d are all different prime numbers.

2.

There's no requirement that the grid in the sieve of Eratosthenes should be a square. In fact, it could be 1 x 10,000 and the method would work just as well.

3.

You talk about the probability of finding a prime number in each region 1-10, 11-100 etc, but the concept of probability in this case doesn't fit in with the primes, which are fixed and there is nothing probable about them. What you mean is, that if you pick a number at random in this range, the probability of it being prime.

4.
Alan Turing is best known for the key role he played his development of the Turing Machine, which decoded messages encrypted on the German 'Enigma' machine

Not only is this badly phrased but it is also wrong. I don't know the name of the machine which decoded the German messages, but it was not called the Turing machine. A Turing machine is an abstract logical concept which Turing used to explore the limits of computability, producing a complete analysis of which problems are computable by every computer and which are not computable by any computer.

5.
Note that only 11 digits are required to express the total number of atoms in the universe!
This is definitely wrong. I've heard that it is 85 digits, but it is certainly much more than 11.

6. I really don't think you've explained the reason for prime number cicadas well at all.
--------------------------------------------------------------------------------------------
Now for the nitpicking:

Another way of describing a prime number is that a prime number is
-->
Another way of describing a prime number is that it is

Eratosthenes was a Greek Mathematician, who -- give Mathematician a small 'm' and get rid of the comma

all the proper multiples of each successive of each (prime) number -->

all the proper multiples of each successive (prime) number

An SI-related unit of magnetic induction, the gauss (also called 'magnetic flux density') is named after him
-->
The gauss, an SI-related unit of magnetic induction (also called 'magnetic flux density'), is named after him

(i.e. 1G = 10-4 Tesla) --> (1G = 10-4 tesla)

of his mathematical discoveries -- add a full stop

he asked, How many prime numbers are there?' -- this needs an opening quote mark before How

probability is spelled wrongly as probabilty in a few places

i.e. as the numbers got bigger -- you should use "that is" rather than "ie" here.

859 page book --> 859-page book

compex variables --> complex variables

"At the start of the 20th Century, the Riemann Hypothesis was one of the world's most intractable mathematical problems, having challenged some of the world's greatest mathematical minds." -- you said almost exactly the same thing in the previous paragraph, so this is repetition.

only five snapshots are known to exist --> only five snapshots of him are known to exist

to hate mirrors becaiuse --> to hate mirrors because

what what to be a long and fruitful collaboration -->
what turned out to be a long and fruitful collaboration

Dates should be in the format DD Month, Year so that 18 February 1918 should be 18 February, 1918

the key role he played his development of the Turing Machine-->
the key role he played in the development of the Turing Machine

a frenetic, if brief mating orgy -- either remove the comma or put another one after brief

Footnote number 3 is empty.

You might like to add to the Freeman Dyson footnote: "His name is also well-known in the Science Fiction world due to his invention of the Dyson sphere."

G

It has peaks and valleys. The Riemann 'zeros' represent the points at which x=0; i.e. where the bases of the mountains are at the table level. What Riemann also discovered was that the 'zeros' all seem to be in a straight line i.e. have the same value of 'z'. This is called the 'critical line'

A full stop is missing.

Now for some nitpicking (Note for B'Elana: that's 'Erbsen-zählen'; don't read any further!).

In your conventions, the zeros are the values (x,z) such that the corresponding y=0, because y is the vertical parameter. The fact that the zeros are all in the a straight line means that all values (x,z) such that the corresponding y is zero are located on a straight line - we can arrange for this to mean that all corresponding 'z' have the same value, but this is usually not the case.

I think that traditionally, we take z to be the vertical value, depending on the pair of parameters (x,y) - and the critical line is the one for which y = 1/2.

What I suggest (to avoid this technical discussion, which would really only confuse everybody) replace x by y in 'the points at which x=0', and remove the 'i.e. have the same value of 'z''.

Gnomon - I was puzzled by the square requirement too in Eratosthene's sieve too, but then I saw the point: once you've done the first line, all what is left in the whole square are prime numbers. It's just a way to say that you can stop at the square root of the maximal number you wish to check, really. Of course the method is actually shape-independent.

And a 1x10,000 grid can be arranged in a square grid, too.

You can tell I'm bored, can't you? Well, time for I think. Good night!

Also, I didn't mean to imply that you HAD to do it as a square grid. It's just that this is probably a natural way of doing it. eg I once taugfht in a specialist school for dyslexic pupils - who have a problem with sequencing - and so we used to get them to write out their times tables as 12 x 12 number grids.

Also, I've dealt with Gnomons 'nits' but not the 'mistakes' which I'll leave till tomorrow I mean later today!

I've just printed this out to read over lunch tomorrow - prime rib

(i wish)

I've now dealt with Gnomon's criticisms on 'Content'. All except the 'bad wording' on cicada. If I get a moment of inspiration I'll try a different form of words.

'The only thing I think it needs is a brief description of how prime numbers underpin cryptography, and the consequences for this if anyone ever found the magic prime number formula... ' (Icy North)

<ok. I've added a 'tail end' to include this.

Oh, the Weizmann Institute? My fiancee is studying there!

And I don't believe that a proof of the Riemann Hypothesis would help much in factorising large integers... Because, really, if you want to use the result for practical purposes, you don't actually need a proof.

Well, I'm not going to argue with Marcus du Sautoy - and that's what he said in the O.U. TV programme on 'Music of the Primes'.

It's not the proof per se - it's the increased understanding of primes that would arise from proving the Riemann Hypothesis.

I really enjoyed this entry.

Nothing to add really, except that I think the machine Turing helped build was called 'Colossus'.