UBASIC – Millennium Bug Fixed – At Last

UBASIC is a marvellous BASIC-like system using high-precision arithmetic, written by Prof. Yuji Kida of Japan.

However, the date function produces CCYY for the year where CC is the century but YY is the 2-digit year with a leading blank!

For example, in 2009 we saw:

Words for long variables 540 (Words for internal calculation 540)
Free text area = 39655 bytes
OK
print date
20 9/12/30/ 9:22:08
OK

But finally, in 2010, it is now fixed:

print date
2010/ 1/25/ 0:19:55
OK

And we only had to wait 10 years!

C241 The Results

The factors of the composite 241-digit number from (16·10²⁴¹-7)/9 = 17₂₄₁ = 17 · C241 have finally emerged. They are three primes with 65-digits, 66-digits and 111-digits respectively:

p65=270337860498008194082459267955\
20615358719149908036271396619108987

p66=122051692513357047795460444698\
080453043250398905366859681372244889 and

p111=316940598147621047292107747704\
251800926330158032587268989314\
536704792625367268739179292577\
795143793534075784267

Whew !

C241 New Lanczos Time – 357 Hours

After advice from Serge Batalov, I stopped the Lanczos run on the 241-digit composite number and did five more days of sieving with GGNFS. This increased the raw relation count from about 102 M to nearly 116 M.

...
Fri Dec 18 17:45:40 2009  found 23488388 hash collisions in 115930392 relations
Fri Dec 18 17:45:55 2009  commencing duplicate removal, pass 2
Fri Dec 18 17:47:58 2009  found 23586813 duplicates and 92343579 unique relations
...

These extra relations enabled Msieve to reduce the matrix size from about 13.2 M down to about 11.3 M, thus considerably reducing the run-time for solution. Here is the reduced time estimate:

The new time in the Lanczos step saves 515 – 357 = 158 hours. The extra sieving took 5 days or 120 hours. That’s an overall saving of 38 hours — a grand total of a day and a half.

C241 Lanczos Time – 515 Hours

My C241 number from Makoto’s list* has finally started the Lanczos step. But at 515 hours, I won’t even get the answer this year.  I did think it would probably be a long calculation after getting past 100 million relations and producing a 13.2M x 13.2M matrix !

...
Sat Dec 12 13:27:37 2009  found 19564136 hash collisions in 102326209 relations
Sat Dec 12 13:27:52 2009  commencing duplicate removal, pass 2
Sat Dec 12 13:29:42 2009  found 19487173 duplicates and 82839036 unique relations
...

Now all we can do is wait. At least the Msieve program provides a checkpoint every 12 (?) hours so we can breathe easy. The Lanczos algorithm is equivalent to inverting a matrix – in this case solving a system of 13.2 million linear equations with 13.2 million variables. Gasp !

To see the full width of the above picture, it is best viewed with a horizontal screen resolution of 1,280 or more. However, if viewing at a lower resolution and you are using Opera, just hit the “-” key a couple of times to shrink the image slightly. “*” will bring you instantly back to your normal resolution.

---

* This composite number is from the partial factorisation of the 242-digit number 177777… (7 repeated 241 times), or:

(16·10²⁴¹-7)/9 = 17₂₄₁ = 17 · C241

See the factorisation website of Makoto Kamada for other incredible results.

KB973525 Causes Visio Viewer to Fail

The Microsoft security update KB973525, issued on Oct 13 2009, fixes some vulnerabilities in ActiveX running under Internet Explorer.

Quoting from that article: “Known Issues. None”

Unfortunately, a serious side-effect is to make Microsoft’s own Visio Viewer refuse to load Visio files. The viewer, which runs as an Add-on within IE, only produces a little square with a red cross (in Windows XP) or a failed-image icon (in Windows 2000). Both the 2003 and the 2007 versions of Visio Viewer fail.

Visio Viewer Failed

Until Microsoft issues an official fix, go to Add/Remove Programs and select KB973525 for removal.

Visio Viewer is then much happier:

Visio Viewer OK

GIMP – Restoring the Layers Dialog

GIMP is an Open Source program for manipulating images. See the About window:

About GIMP

When starting the program, several windows are opened including (usually) a Layers Dialog box which gives you a way of manipulating the layers of a composition. When closing, however, the temptation is to close all the windows visible.

Big mistake.

All you need to do is to close the main window (the one with the File menu).

By closing the Layers Dialog before the main window, next time GIMP opens it will not display that dialog.

In previous editions, there was a Dialog entry under File to help you to recover the missing window. However, in the current (2.6.7) version, you must go to Windows | Dockable Dialogs | Layers to restore sanity.

GIMP missing Layers options

Windows – Internet Sharing

After some hardware shuffling, my LAN computers could not access the internet. The main XP computer with the ADSL2+ modem connected fine.

Google to the rescue – that takes me to a Knowledge Base article by Microsoft.

On the client computer
To connect to the Internet by using the shared connection, you must confirm the LAN adapter IP configuration, and then configure the client computer. To confirm the LAN adapter IP configuration, follow these steps:

1. Log on to the client computer as Administrator or as Owner.
2. Click Start, and then click Control Panel.
3. Click Network and Internet Connections.
4. Click Network Connections.
5. Right-click Local Area Connection, and then click Properties.
6. Click the General tab, click Internet Protocol (TCP/IP) in the This connection uses the following items list, and then click Properties.
7. In the Internet Protocol (TCP/IP) Properties dialog box, click Obtain an IP address automatically (if it is not already selected), and then click OK. Note You can also assign a unique static IP address in the range of 192.168.0.2 to 192.168.0.254. For example, you can assign the following static IP address, subnet mask, and default gateway:

   IP Address 192.168.0.2
   Subnet mask 255.255.255.0
   Default gateway 192.168.0.1

8. In the Local Area Connection Properties dialog box, click OK.
9. Quit Control Panel.

Unfortunately, they don’t say anything about setting the DNS server address, which makes all the difference:

TCP properties

A Google Coincidence

Here’s a little coincidence.  In the quiet suburb of Bexley in Sydney, Google Earth caught two cars in a local roundabout.

Roundabout at Bexley in Sydney

Not earth-shattering, but very interesting…

A Google Record?

After publishing “The 7-Pointed Magic Star Problem”, below, I checked with Google to find similar entries.

My Blog entry was already found by Google – after just 14 minutes. A Google Record?

Amazing.

The 7-Pointed Magic Star Problem

#
#   Solve the 7-Pointed Magic Star Problem
#
#   Numbers 1-14 give equal sums in each of 7 lines making up
#   the star shape below.  Eg: B+C+D+E = 30, B+F+J+M = 30, etc.
#
#                 A
#
#       B     C       D    E
#
#        F                G
#     H                      I
#          J             K
#                 L
#            M         N
#
#

This is a similar problem to the 6-Pointed Magic Star Problem, below.

We now have fourteen unknowns with seven equations. Choosing seven values gives 14 x 13 x 12 x 11 x 10 x 9 x 8 (14 choices of A x 13 choices of B etc. or 17,297,280) possible solutions.

Many of these choices give values which are less than 1 or greater than 14 for some of the letters. We also must eliminate illegal combinations where some numbers are duplicated. Finally we get a total of 1,008 solutions.

Counting 7 rotations and 2 reflections as equivalent, we find that there are just (1008 / 14) or 72 unique solutions.

Here are the first few:

 N   a  b  c  d  e  f  g  h  i  j  k  l  m  n                     P V

 1:  1  2  4 10 14 13  8 12 11  6  3  7  9  5 Peak: 54 Valley: 51
 2:  1  2  5 14  9 13  7 11  8  3  4  6 12 10 Peak: 53 Valley: 52
 3:  1  2  8 14  6 11 12 10  3  4  5  9 13  7 Peak: 42 Valley: 63
 4:  1  2 10 14  4 11  6  8  9 12 13  3  5  7 Peak: 36 Valley: 69
 5:  1  2 10 14  4 13 12  6  3  8  9 11  7  5 Peak: 28 Valley: 77
 6:  1  3  5 13  9 10 12 14  4  6  7  8 11  2 Peak: 44 Valley: 61
 7:  1  3  6 14  7 12 10 11  5  2  4  8 13  9 Peak: 49 Valley: 56
 8:  1  3  8 13  6  7 12 14  4  9 10  5 11  2 Peak: 41 Valley: 64
 9:  1  3  9 14  4 12 13  8  2  5  7 11 10  6 Peak: 34 Valley: 71
10:  1  3 11 14  2 13  7  5  8 10 12  6  4  9 Peak: 32 Valley: 73
11:  1  3 11 14  2 13  9  5  6 10 12  8  4  7 Peak: 28 Valley: 77
12:  1  4  5 12  9 13  3 11 14  7  8  2  6 10 Peak: 55 Valley: 50
13:  1  4  6  8 12 10  7 13 14  5  2  3 11  9 Peak: 64 Valley: 41
14:  1  4  7 14  5 12 13 10  2  6  9 11  8  3 Peak: 33 Valley: 72
....

This time there are no solutions where the Peak or Valley sums are equal to 30.

[ Peak Sum = A + E + I + N + M + H + B, Valley Sum = D + G + K + L + J + F + C ]

CPU stuck to heatsink

I have had that PC since 2001 and it overheated in January 2009 (southern Summer). Naturally I tried to check the contact between CPU (an AMD Athlon 64 3400+) and heatsink. In my enthusiasm, I lifted out the heatsink with the CPU still attached.

They were so tightly joined that I couldn’t think of a safe way to separate them. Fingers and hands were no match. So of course I left it on the workbench. There was no way to replace the pair of them onto the motherboard because the little plastic arm could not be raised without touching the huge heatsink.

A while later, another PC had dry heat paste problems. I tried wiping away the paste with Meths and it worked!

Unfortunately, on my PC, no amount of wiping around the tight join with a brush dipped in Meths did any good. In desparation I found an old shallow dish and soaked the CPU and the bottom of the heatsink in the Meths.

After 24 hours I still couldn’t shift it.

Finally after 48 hours, I gave it a moderate twist and it came free. Joy.

After a thorough clean and a careful reassembly (with new heat paste), the PC is now alive and well.

With a lot of updating to do. Opera 9.64 and Firefox 3.5.2 just to name two. And Microsoft, of course:

What a relief!

The 6-Pointed Magic Star Problem

#
#   Solve the 6-Pointed Magic Star Problem
#
#   Use the numbers 1-12 to give equal sums in each of 6 lines making
#   up the star shape below.  Eg: B+C+D+E = 26, B+F+I+L = 26, etc.
#
#                  A
#
#     B       C        D      E
#
#         F               G
#
#     H       I        J      K
#
#                  L
#

This is a very old puzzle, first proposed by Henry E. Dudeney and catalogued by Donald E. Knuth with the entry:

+50(15)210 X261 A star puzzle: Magic 6-star of {1,2,…,12} with sums 26

meaning: Volume 50, (1915), page 210, puzzle number X261.

This can be considered a problem in 12 unknowns with only 6 equations (the 6 straight lines making up the figure). There are therefore apparently 6 degrees of freedom. A straight-forward approach would be to choose A, B, C, D, F and G, (E must be equal to 26 – B – C – D, of course) and then calculate the other letters from the obvious relations. This would appear to give 12 x 11 x 10 x 9 x 8 x 7 solutions (12 choices for A, 11 for B etc) or 665,280 in all.

Unfortunately, many of these choices give values which are less than 1 or greater than 12 for some letters E or H – L. When these are eliminated, there are still many illegal combinations left where some numbers are duplicated. Finally the number of solutions is whittled down to 960.

But the figure has 12-fold symmetry (6 rotations x 2 reflections), so we find the number of unique solutions to be (960 / 12) or just 80.

Hardly any deep mathematical knowledge was required, just brute-force and symmetry.

We have written a simple Perl program to produce the 80 solutions in 5 seconds of PC elapsed time and invite reader solutions, too.

Here are the first few we have found:

 N   a  b  c  d  e  f  g  h  i  j  k  l                     P V

 1:  1  2  4 12  8 10  6 11  5  3  7  9 Peak: 38 Valley: 40
 2:  1  2  6 10  8 12  4  7  3  5 11  9 Peak: 38 Valley: 40
 3:  1  2  7 11  6  8  5 10  4  3  9 12 Peak: 40 Valley: 38
 4:  1  2  7 12  5 10  4  8  3  6  9 11 Peak: 36 Valley: 42
 5:  1  2  8  9  7 11  4  6  3  5 12 10 Peak: 38 Valley: 40
 6:  1  2  8 10  6 12  4  5  3  7 11  9 Peak: 34 Valley: 44
 7:  1  2  9 12  3  6  8 10  7  4  5 11 Peak: 32 Valley: 46
 8:  1  2 10 11  3  8  5  7  4  6  9 12 Peak: 34 Valley: 44
 9:  1  3  4  8 11 12  7  9  5  2 10  6 Peak: 40 Valley: 38
10:  1  3  5 11  7 12  4  8  2  6 10  9 Peak: 38 Valley: 40
11:  1  3  6 12  5 11  4  8  2  7  9 10 Peak: 36 Valley: 42
12:  1  3  7 11  5  6 10 12  8  2  4  9 Peak: 34 Valley: 44
13:  1  3  7 11  5 12  4  6  2  8 10  9 Peak: 34 Valley: 44
14:  1  3  7 12  4  8 11 10  9  5  2  6 Peak: 26 Valley: 52 *
....

A little curiosity: solution number 14 shows the sum of the Peaks also to be 26. Six solutions have this property; another six have the sum of the Valleys to be 26.

[ Peak Sum = A + E + K + L + H + B, Valley Sum = D + G + J + I + F + C ]

Automatic reboot – XP

Here is the typical XP message after the reboot and Login:

It’s a good thing that hospitals don’t rely on this software.

Automatic reboot – how Linux does it

A few minutes ago, my Fedora 11 box asked if it could install 11 updates (and it listed updates to Firefox and other browsers).  I said OK. Then the little red indicator appeared. Hover over it; take a screen-shot:

It’s in the middle of more calculations at the moment, so I’ll wait 30 minutes or so until I can interrupt it. Then restart Fedora. Then resume the calculations.

That’s how a sane OS behaves.

Automatic reboot – Windows 7

The outrageous feature of Windows XP automatically rebooting after some important Microsoft Updates continues with Windows 7.

It happened early this morning, July 30 2009, after the installation of the “Cumulative Security Update for Internet Explorer 8 for Windows 7 Release Candidate (KB972260). As one paragraph says:

Overview
Security issues have been identified that could allow an attacker to compromise a computer running Microsoft Internet Explorer and gain control over it. You can help protect your computer by installing this update from Microsoft. After you install this item, you may have to restart your computer. [Bob: Underline added]

A 2 ½ hour calculation solving a 1,500,000 × 1,500,00 linear matrix was interrupted. Luckily this was not a 60 hour calculation (220 digit factorisations often take this long on the matrix inversion step).

Windows 7 64-bit pricing

No mention of different prices for 32-bit and 64-bit versions. Seems that both will be provided in the boxed set, but you only get the Product Key for the one you pay for.

Makes sense.

Interesting to see what the Australian prices will be. At 80 cents US to $1 AUD, the Full Ultimate price of $US 319, gives $AUD 398 – a very convenient (large) number.

Windows 7 prices announced by Microsoft

June 25 2009, Microsoft releases the U.S. retail prices for Windows 7.

For full retail versions:

• Home Premium Full: $199
• Professional Full: $299
• Ultimate Full: $319

For retail upgrades:

• Home Premium Upgrade: $119
• Professional Upgrade: $199
• Ultimate Upgrade: $219

At these prices, I don’t think I’ll be rushing out to buy.

When my RC1 version of Windows 7 Ultimate runs out next March 2010 I’ll be upgrading to the most stable Linux version I’ve ever used (Fedora 11).

Win 7 expiry screen-shot

Here’s the screen-shot showing how Win 7, Build 7000 will expire in one more days [sic]:

The old Win 7, Build 7000 has expired

The original Windows 7 Beta (Build 7000) expired on the 2nd of July 2009 (well, the expiry messages said “3 days”, “2 days” and “1 days” to go).  Yes, they really did say “1 days” !

What they meant was that the OS would start shutting down every 2 hours after that date.  This would go on for a month and finally go unauthorised or unactivated in August 2009.

Luckily I already had the RC1 version (Build 7100) which goes until March 2010.  I installed it onto the other 250 GB partition and had easy access to my data from the 7000 partition.

I am very impressed with Win 7 (never a crash).

The only small problem I had was getting a driver for my old Realtek PCI Ethernet Adapter (the one with the co-ax cable – you remember them ?).  Anyway, a Google Search said that Win 7 will work with the driver from Win 2000 – and it did.  After installing it, Win 7 found the internet within a few seconds. Wow !

Introducing blogging to a PC User Group

This is set up as an example blog for a PC User Group.  I’m using WordPress because of the great features and themes available.

The group may or may not take up blogging, but at least we will get to see the easy way of posting great-looking text without the complexity of creating personal web-sites and doing Html coding (cough, cough).