My best to you <Dom>. Great to see your comments at the Live gamepage. "It's been a pleasure again today."

- I say, my man! Yes, you, the jailer chappie! The, um, *screw*, I believe? Kindly send for the *warden* at once. I wish to have this property *valued*.

'Why?', my good fellow? Why? Are you *insane*? I want it valued so that I can *buy* it, obviously. Investing in prison real estate will pay vast dividends in future, as more and more people are locked up for trivial 'offences' such as double parking, self medication, and banking.

This isn't quite mathematics -- it's trivial, and I skip several proofs. But it isn't numerology either: the numbers don't come glued to any semantics, and I don't try to derive 'meaning' from them. I *could* actually produce proofs where needed, but they're elementary and/or trivial and yet would need a lot of space. This medium isn't ideal for working with exponents, so I use an eccentric shorthand method of describing squares.

Prime numbers (those >3, to be specific) come in two varieties: those of the form 4n+1 and those of the form 4n-1 (aka 4n+3). To labour the obvious, numbers of the form 4n+2 and 4n+0 must be even, hence nonprime. That leaves 4n+1 and 4n+3 (aka 4n-1).

It turns out that every prime of the form 4n+1 is equal to the sum of two squares; and no prime of the form 4n-1 is equal to the sum of two squares.

SOS is an acronym for 'sum of squares' and this is the reason for splitting primes into two groups this way (there are other ways of grouping them, eg 6n+1 and 6n-1, with different distinguishing properties).

We concentrate on 4n+1 primes, each the sum of two squares in exactly one way. The sequence begins 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149 ... the list is infinite, and every number can be expressed as an ordered pair, eg 2017 = (44, 9) -- because 44^2 = 1936, and 9^2 = 81, and 1936 + 81 = 2017. The next date, incidentally, to be a prime of form 4n+1.

I'll skip over all sorts of interesting qualities of this sequence - it's intricately linked to the Fibonacci sequence, for example, if you want to explore that - in order to define some nonstandard symbols and terminology.

To pick one number, 89 is the sum of the squares of 8 and 5: 89 = 64 + 25 = 8^2 + 5^2. To avoid a jungle of carets (ie, too many cases of p^2 etc) I'm going to write each SOS as an ordered pair. Like this: instead of 5 = 2^2 + 1^2
we write simply
5 = (2, 1)

The other 4n+1 primes fall into line like this:
5 = (2, 1)
13 = (3, 2)
17 = (4, 1)
29 = (5, 2)
37 = (6, 1) and so on.

If you multiply two of these 4n+1 primes together you get a compound number which is the sum of two squares in two different ways. Basic algebra shows how this works, but I'll skip the proof. The combinatorial rule is

If p and q are primes of form 4n+1, and p = (a, b) and q = (c, d), then the product pq is expressible like so: pq = (ac+bd, ad-bc) = (ac-bd, ad+bc)

Now for today's trick. The lowest 4n+1 prime > 14000 is 14009. I want to multiply 14009 by some unknown whole number, k, such that 14009k equals a square, plus one. Or

14009 x k = (a, 1)

To find k -- actually the lowest value of k, which can take on an infinite range of values -- first express 14009 as a sum of squares:

14009 = (115, 28)

Next, find multiples of 115 and 28 which differ by 1 -- various algorithms will solve this. It turns out that

115 x 9 = 1035
28 x 37 = 1036

Now, k equals the sum of the squares of these factors, so:

k = (37, 9) = 1369 + 81 = 1450

check this:
14009 x 1450 = 20313050
= 4507^2 + 1
= (4507, 1)

Now the final cool detour to produce a second value of k, complementary to the first.

14009 - 4507 = 9502
9502^2 + 1 = 90288005
= 14009 x 6445

6445 is our 2nd value of k. This is clearly not a prime: it factorizes as 6445 = 5 x 1289
6445 = (2, 1)*(35, 8)
= (78, 19) = (62, 51)

One of these pairs should satisfy our previous conditions. And so:

28 x 78 = 2184
115 x 19 = 2185

Cue eeeh bleedin dee.

I'll just zip back to 2017 to tidy up.
2017 = (44, 9)
An easy one: (44 x 1) + 1 = 45 = 9 x 5
(5, 1) = 26
26 x 2017 = (229, 1)
And its complement:
2017 - 229 = 1788
(1788, 1) = 2017 x 1585
1585 = 5 x 317 = (2, 1)*(14, 11)
= (28-11, 22+14) = (28+11, 22-14)
= (17, 36) = (39, 8)
and 39 x 9 = 351 = [44 x 8] - 1.

- He's doing it again, isn't he? Well, I guess as long as he doesn't frighten the horses ...

[*noises off ... long, terrified whinny, like a Houhynym having a very bad trip ... other horses go 'neigh, neigh' but they're obviously on the leading edge of panic.*]

TIMING

I was born on the the foiteenth of Settembre, so that's a sure hit with me.

And at the time of typing this it's : <14014>

Meanwhile, it's time for a dose of <Emergency Scholastic Theology>. Like insulin, it was first extracted from sheep and such before they learned to synthesize it chemically.

The big questions include *intellectual property*, *copyright*, *narratology* and *ownership of a chess game*.

In Scholastic terms, these all fall under the dogmatic zone known as <Relics of Saint Nigel>.

To begin, we invoke a short prayer by Saint Shakespeare Hobbes:

<"The Short, dear Brutus
Lies not with the Stars,
But with the Poor and Solitary.">

I have never put anyone on ignore and don't plan to start now.

Bill - aka William Burroughs, author of Naked Lunch, Soft Machine, etc - is also somebody I respect. The quote about chess as a waste of a man's mind actually turned up as CG's quote of the day, about a week ago. I found it in his collected letters, and <mack> sent it to CG central, along with some other offbeat chess quotes.

In its full context, i'ts clear that Burroughs investigated chess sufficiently far to see how its depths could take over everything else in life. It is inherently obsessional -- and Burroughs knew all about addiction. So the line isn't a put-down based on ignorance, but on understanding.

These are good things to discuss. Here, anything goes.

"I can't paint and I can't f**k and I'm angry all the time. Now I know how a critic must feel."

Which was this: with the Conservatives returning to power in Britain, it's time for one of the songs inspired by their previous triumph.

Elvis Costello's 'Tramp the Dirt Down' would be an obvious choice. But since it concerns what he'd like to do to Mrs Thatcher's grave, it might be in, heh, bad taste.

And we can't have that. So the winner is Momus, and the song is called 'Sex for the Disabled'.

Bad taste? Moi?

"Before the accident/ Before '79/ Before the wheelchair/ That was such a different time ..."

Got your post today. I don't monitor the forum that much anymore. I'm wondering if there's another GM ready anytime soon to play us again.

wasnt there at the appointment. I got in the reception hall, where there is a chess shop and the check in desk. I asked one of the guards to get in looking for my man,

but he refiused, explaining that he cant move from his place. in that moment the woman from the shop came to me and gave me an invitation card!(I've twice offered

caffee to all the staff, and maybe she remembered that; I did that because I enterd to see the first game of the match thanks to ouer prime minister Boyko Borisov,

whom I asked to help us enter like standing spectators - there were no more tickets, and he told to the guards to let mi in withe my friend). after the official ceremony of the closing day, we mixed up all together, taking autographs, short intervews and, of course, plenty of photos. and in that

hubbub sudenly I saw the bulgarian banner stamped on the floor, I've picked it up and wear it with pride. then I spoke with Vishy for a while, I took an autographe

from Topa and Silvio - nobody told me nothing. so I said goodby and further success to Vishy and went off. I kept wearing the tricolor strip and went home with the

dignity of a doge. my father(88) and my mother(86) were impressed by the story, more - we found out that on the strip there was a writing: 'world chess champion 2010'!

after the euphory passed, my mother said: '' if this belongs to Mr Anand, you must go to the hotel and give back him the strip!'' so I went to the hotel, some 700

yards away, and said to the young receptionist, that I must give personally a strip to Mr Anand, and I'v left my phone nomber for contact. nobody phoned till 11 am of

next day. I was worried, that's why I phoned to my man - Mr Radoslav Atanasov, asking him what to do: he told me, if this is the Vishi's champion's strip, you go and

you give it back to him! so I did: arriving in the hotel, I saw Aruna and a white haired man(probably Anand's manager) in the hall; I went to them and explained the

situation; Aruna said that this wasnt Anand's strip, probably this was Topa's; in this moment the man said: ''it's OK for me''(I instantly understood what he wanted to

say to Aruna - take it for me!) unfortunately for me, she agreed and told me -''thankyou very mutch, I'll take it''!!!! I couldnt react to this flagrant robbery! I

quit totaly desgusted: people, having just taken 1,2 million euros have stollen from me a trophy, I totaly deserved! I felt very bad: first of all my mother has

betried me, forcing me to give the strip back: for once the bird has landed on my shoulder and she dismissed it!!!;second; the so called ''western'' civilisation''

disappointed me enormously and, third - I felt a week, deprived from spirit man, unable to react: but how should I, this was Anand's wife!! the partner of a God!!! I

Of course you could probably have kept it, but for what? To show people, as a trophy?

I've been at two world championship matches - Kasparov vs Karpov and Kasparov vs Short, both in London. I've also met and interviewed many 'famous' people, writers, actors, etc. I have almost no souvenirs or objects, because I never cared about getting signatures or trophies.

"THE SICILIAN VESPERS" starring User: crawfb5:

http://www.youtube.com/watch?v=mVJ_...

Chess is a unique game due to its rich history- whenever any of us plays, we follow in the footsteps of past Masters. This is the story of Larry Crawford, a strong player who recently "played in to" a very famous, and interesting, incident in Chess History: the "Sicilian Vespers" episode between the Russians and the Argentines at the Goteborg Interzonal in 1955. The story continued a few years later in 1958 when a 15 year old Bobby Fischer stunned Gligoric by reviving the "Sicilian Vespers" line at the Potoroz Interzonal in 1958.

I urge all chessplayers to examine their games against a good database to see which famous episodes of Chess History YOU might be participating in!!

Here is the PGN file of Crawford's game:

[Event "Challenge"]
[Site "http://www.queenalice.com/game.php?..."] [Date "2010.2.15"] [Round "-"]
[White "crawfb5"]
[Black "borghese"]
[Result "1/2-1/2"]
[WhiteElo "2237"]
[BlackElo "2405"]
[ECO "B98"]

Incidentally, it's hard to play <noughts and crosses> without repeating yourself, never mind other people.