Special whole numbers...

[mfgoode]

Originally Posted by nibble4bits

Oooooooooh you mean because it's a ZIP? Or because it has BASIC code in it so it's in a blanket filter?

I'm so clever I got a virus into a plain text file that only notepad knows how to load. j/k Load it in Edit.com or Notepad.exe to see if those 3 text files are safe. I bet you'll just say "stupid AV strikes again!" >:)

But it's funny that people think their AV tools are always right. Not that I'm saying you couldn't figure that out.


<Edit> Oh yeah, that's used in physics as well. It's this: Sum of n^-3 for n=0 to infinite.

Had I read your post earlier I would have given the name of the virus as well when it was tracked down and deleted from the virus vault.
Sum of n^-3 yeah. Better known as Z (3)
Mally

[Kees]

Surely not n=0 to infinity

Find the number that is a permutation of 123456789, and when factored has the smallest largest primefactor.

For instance

123456789 = 3^2*3607*3803 -> 3803
234567891 = 3^2*109*157*1523 -> 1523

[tom11784]

we have a tie

619573248 = ** --> 7
948721536 = ** --> 7

keep in mind this was done with a C++ program that took about 10 minutes to work through once written, but it also returned 3 invalid results, so this may be an incomplete list

note these numbers were verified by using a factoring calculator

[nibble4bits]

Whole numbers, eh? That was a decimal. :P

OK Try these related numbers: 2, either 9 or 12, either 209 or 139 or 232 or 184, either 62658 or 34398. Note that these are just the ones I felt like finding.

How would I generate an arbitarly high number in this set?

First hint:

Again this is a sequence relation.
Try conversion to another base.
Notice how the numbers grow... hehe Cute, huh?


2nd hint:

Base 16 should make this clearer.
There's a base that gives this away if you've been reading this thread.




I fail to see how this is a virus:

REM Counts string frequency for 2-digit strings in a larger string.
CLS
DIM StringCount(0 TO 99), CodeKey$(0 TO 9)
A$ = "0001020304050607080910111213141516171819202122232425262728293031323334"
A$ = A$ + "35363738394041424344454647484950515253545556575859606162636465666"
A$ = A$ + "76869707172737475767778798081828384858687888990919293949596979899"
B$ = A$
CodeKey$(0) = "4"
CodeKey$(1) = "0"
CodeKey$(2) = "7"
CodeKey$(3) = "5"
CodeKey$(4) = "9"
CodeKey$(5) = "2"
CodeKey$(6) = "6"
CodeKey$(7) = "3"
CodeKey$(8) = "1"
CodeKey$(9) = "8"


REM Counts the number of times a 2-digit appears.
FOR i = 1 TO LEN(A$) - 1
StringCount(VAL(MID$(A$, i, 2))) = StringCount(VAL(MID$(A$, i, 2))) + 1
NEXT i
REM Special case for wrap-around at positions 1 and 100.
i = 10 * VAL(MID$(A$, 100, 1)) + VAL(MID$(A$, 1, 1))
StringCount(i) = StringCount(i) + 1

INPUT i
FOR i = 0 TO 9
IF StringCount(i) = 0 THEN PRINT "*";
IF StringCount(i) = 1 THEN PRINT "!";
IF StringCount(i) > 1 THEN PRINT " ";
PRINT " 0"; RIGHT$(STR$(i), 1); " ="; StringCount(i), ;
NEXT i
FOR i = 10 TO 99
IF StringCount(i) = 0 THEN PRINT "*";
IF StringCount(i) = 1 THEN PRINT "!";
IF StringCount(i) > 1 THEN PRINT " ";
PRINT i; "="; StringCount(i), ;
NEXT i
PRINT "Length in bytes: "; LEN(A$)
PRINT "Efficiency (1=no repeated 2-digit strings): "; (100 / LEN(A$))

FOR i = 1 TO LEN(A$)
MID$(B$, 1 + LEN(A$) - i, 1) = MID$(A$, i, 1)
MID$(B$, 1 + LEN(A$) - i, 1) = CodeKey$(VAL(MID$(B$, 1 + LEN(A$) - i, 1)))
NEXT i
REM PRINT A$
PRINT B$

It's maybe a little obfusicating but I doubt your AV is right since I wrote it myself and it contains no code to copy itself. Bow to the oh so superior twin gods McAfee and Norton of mount security. LOL

[fetofs]

Originally Posted by mfgoode

On opening your attachment my browser's anti virus software alerted me of a virus in your files. :surprised
Mally

Which AV do you use?

[xilman]

Originally Posted by mfgoode

See what you can make of this.
The reciprocal of this number 137 figured early in the theory of Relativity and Quantum Electrodynamics. This dimensional constant (DC) was obtained from the formula 2**e^2hc = 1/137 known as the constant of fine structure.

What I make of it is that you've either misunderstood the subject or you have mistyped your contribution.

For a start, \alpha is a dimensionless constant. It essentially specifies the strength of the electromagnetic interaction at zero energy, independently of the units used. The technical term is "coupling constant of the EM interaction". Note that the strength of the EM interaction is energy dependent. At higher energies its value rises.

Secondly, 1/\alpha is not 137. It's measured value is 137.03599911 \pm 4.6e-7


Paul

[mfgoode]

Originally Posted by Kees

Surely not n=0 to infinity

Find the number that is a permutation of 123456789, and when factored has the smallest largest primefactor.

For instance

123456789 = 3^2*3607*3803 -> 3803
234567891 = 3^2*109*157*1523 -> 1523

Correction noted!
The number of permutations of 123456789 is 362880 . These have to be
programmed as Tom has done and that too it took ten minutes.
Interesting Tom to take all the trouble and find a tie at 7

To compensate here is a trick to try on friends/students
Take the number 12345679 and ask her/him to select her favourite digit.
Whichever is picked mentally multiply it by 9 and
put it under the given number. Being fond of that particular number tell her you will multiply the two and give her a string of her favourite digit
Example:say 4 is selected Multiply by 9 getting 36. You will get a string of
4's when 12345679 * 36 =444444444
Take 7: 9*7 =63 so 12345679 *63 = 777777777.
Mally


w

[mfgoode]

Originally Posted by fetofs

Which AV do you use?

I use AVG and Norton and Spyware and Adware plus accounts with MSN, Yahoo, Gmail, Rediffmail which have their own built in AV.
Mally

[mfgoode]

Originally Posted by xilman

What I make of it is that you've either misunderstood the subject or you have mistyped your contribution.

For a start, \alpha is a dimensionless constant. It essentially specifies the strength of the electromagnetic interaction at zero energy, independently of the units used. The technical term is "coupling constant of the EM interaction". Note that the strength of the EM interaction is energy dependent. At higher energies its value rises.

Secondly, 1/\alpha is not 137. It's measured value is 137.03599911 \pm 4.6e-7


Paul

:surprised
Hey Paul: Do you think I can concoct this in my own brain? Far from it!
If it is dimensionless I presume that h = T/L as c= L/T and they both cancel out . But I will check my source. I think its a book written by de Broglie himself one of the active pioneers of Relativity.
Subsequently Einstein wrote this constant off saying it was his greatest mistake. Ref: news item in the TOI.
I dont know if anyone else resurrected it after that!
Mally
P.S. I wrote a full item on this constant. Maybe its in the archives.

[xilman]

Originally Posted by mfgoode

Subsequently Einstein wrote this constant off saying it was his greatest mistake. Ref: news item in the TOI.

Again, you are wrong.

Einstein proclaimed the cosmological constant as his greatest mistake. The fine structure constant is not the same thing as all. Given that there is no theoretical justification for the cosmological constant, as far as I know, there is no known relationship between the two.

Brief history: Einstein introduced the CC so that he could produce a solution to his field equations that described a static universe. The universe was subsequently discovered not to be static, so he removed the constant and issued his famous complaint. Much later, observations of the distant universe have suggested to some cosmologists that the CC is needed after all. The recent and popular name for the CC is "dark energy".


Paul

[xilman]

Originally Posted by mfgoode

If it is dimensionless I presume that h = T/L as c= L/T and they both cancel out . But I will check my source.

The FSC, or \alpha, is defined to be (e^2)/(hbar * c) / (4 * \pi *\epsilon_0)

e has dimension of C (coulombs)
hbar has dimension J s (Joule seconds)
c has dimension m/s (metres per second)
\epsilon_0 has dimension F/m (Farads per meter)

Both other quantities (4 and \pi) are dimensionless.

So the units of \alpha are (C^2) (J^{-1} s^{-1}) (m^{-1} s) (m F^{-1})

Collecting terms, we get C^2 J^{-1} F^{-1}


However, none of coulombs, joules and farads are fundamental units. The dimensions are:


C = A s (Ampere seconds)
J = kg m^2 s^{-2} (kilogram meters squared per seconds squared)
F = m^{-2} kg^{-1} s^4 A^2


So C^2 is A^2 s^2
J^{-1} is kg^{-1} m^{-2} s^2
F^{-1} is m^2 kg s^{-4} A^{-2}


Multiplying out, we find that \alpha is dimensionless, as I claimed.


Paul